Ejercicio 3. Aplica las leyes de los exponentes de potencia elevada a otra potencia y de producto,
para simplificar los siguientes ejercicios
Answers
Aplicando las leyes de los exponentes de potencia, los resultados son los siguientes:
[tex]2097152[/tex] [tex]\frac{1}{729}[/tex] [tex]b^{12}[/tex] [tex]x^{24}[/tex][tex]x^{\frac{6}{5} }[/tex][tex]3600[/tex][tex]a^{6}\cdot b^{10}\cdot c^{-8}[/tex][tex]200\cdot x^{19}[/tex][tex]108\cdot y^{6}[/tex]En este ejercicio debemos aplicar cualesquiera de las siguientes propiedades asociadas a los exponentes:
(i) [tex](a^{b})^{c} = a^{b\cdot c}[/tex]
(ii) [tex]a^{c}\cdot b^{c} = (a\cdot b)^{c}[/tex]
(iii) [tex]a^{-b} = \frac{1}{a^{b}}[/tex]
(iv) [tex]a^{b} = a^{b}[/tex], donde [tex]a[/tex] es negativo o positivo y [tex]b[/tex] es par.
(v) [tex](-a)^{b} = -a^{b}[/tex], donde [tex]a[/tex] es positivo y [tex]b[/tex] es impar.
(vi) [tex]a^{b}\cdot a^{c} = a^{b+c}[/tex]
A continuación, tenemos los siguientes resultados:
a) [tex](2^{3})^{7} = 8^{7} = 2097152[/tex]
b) [tex](3^{3})^{-2} = 3^{-6} = \frac{1}{729}[/tex]
c) [tex](b^{3})^{4}=b^{12}[/tex]
d) [tex][(x^{2})^{3}]^{4} = (x^{6})^{4} = x^{24}[/tex]
e) [tex]\left(x^{\frac{3}{5} }\right)^{2} = x^{\frac{6}{5} }[/tex]
f) [tex](3\cdot 4\cdot 2)^{5} = 3^{2}\cdot 4^{2}\cdot 5^{2} = 9\cdot 16\cdot 25 = 3600[/tex]
g) [tex](a^{3}\cdot b^{5}\cdot c^{-4})^{2} = (a^{3})^{2}\cdot (b^{5})^{2}\cdot (c^{-4})^{2} = a^{6}\cdot b^{10}\cdot c^{-8}[/tex]
h) [tex](2\cdot x^{5})^{3}\cdot (-5\cdot x^{2})^{2} = (2^{3}\cdot x^{15})\cdot [(-5)^{2}\cdot x^{4}] = (8\cdot x^{15})\cdot (25\cdot x^{4}) = (8\cdot 25)\cdot x^{19} = 200\cdot x^{19}[/tex]
i) [tex]\left(3\cdot y^{\frac{2}{3} }\right)^{3}\cdot (2\cdot y^{2})^{2} = (27\cdot y^{2})\cdot (4\cdot y^{4}) = 108\cdot y^{6}[/tex]
Invitamos cordialmente a consultar esta pregunta sobre potencias: https://brainly.com/question/24239709
Related Questions
42 43 45 ? 52
23 ? 33 38 43
Find the question marks
Answers
Answer:
48, 28 respectively
Step-by-step explanation:
You would find the pattern for both.
1) 42, 43, 45, ?, 52
the pattern is +1, +2, +3, +4
42 + 1 = 43 +2 = 45 + 3 = 48 + 4 = 52
42, 43, 45, 48, 52
2) 23, ?, 33, 38, 43
the pattern is to add 5
23 + 5 = 28 + 5 = 33 + 5 = 38 + 5 = 43
23, 28, 33, 38, 43
A 10 -foot ladder is leaning on a tree. The bottom of the ladder on the ground at a distance of 6 feet from the base of the tree. The base of the tree and the ground form a right angle as shown.
What is the distance, in feet, between the ground and the top of the ladder?
Answers
The distance, in feet, between the ground and the top of the ladder is 8 feet.
The diagram formed will be a right triangle having the hypotenuse, adjacent and opposite sides
To get the distance, in feet, between the ground and the top of the ladder, we will use the Pythagoras theorem as shown:
hyp² = opp² + adj²Given the following sides
length of ladder = hyp = 10footdistance from ladder to the base = adjacent = 6 feetSubstitute the given parameters into the formula to have:
10² = opp² + 6²
opp²=100 - 36
opp² = 64
opp = 8feet
Hence the distance, in feet, between the ground and the top of the ladder is 8 feet.
Learn more on pythagoras theorem here: https://brainly.com/question/2938476
plz solve this!!!!!!
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Answer:
where is the question?......
Choose SSS, SAS, or neither to compare
these two triangles.
5
th
出
A
B
с
SSS
SAS
neither
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all sides are congruent!:)
100 POINTS FOR THIS!!!
Answers
Answer:
m∠EFD = 90°
m∠EHF = 127°
m∠HFG = 56°
m∠G = 71°
m∠E = 19°
Step-by-step explanation:
From inspection of the given diagram, line segment GD is a straight line and m∠EFG= 90°.
Angles on a straight line sum to 180°:
⇒ m∠EFG + m∠EFD = 180°
⇒ 90° + m∠EFD = 180°
⇒ 90° + m∠EFD - 90° = 180° - 90°
⇒ m∠EFD = 90°
Angles on a straight line sum to 180°:
⇒ m∠EHF + m∠FHG = 180°
⇒ m∠EHF + 53° = 180°
⇒ m∠EHF + 53° - 53° = 180° - 53°
⇒ m∠EHF = 127°
From inspection of the given diagram, m∠EFH and m∠HFG form a right angle:
⇒ m∠EFH + m∠HFG = 90°
⇒ 34° + m∠HFG = 90°
⇒ 34° + m∠HFG - 34° = 90° - 34°
⇒ m∠HFG = 56°
Interior angles of a triangle sum to 180°:
⇒ m∠HFG + m∠GHF + m∠G = 180°
⇒ 56° + 53° + m∠G = 180°
⇒ 109° + m∠G = 180°
⇒ 109° + m∠G - 109° = 180° - 109°
⇒ m∠G = 71°
Interior angles of a triangle sum to 180°:
⇒ m∠E + m∠EFH + m∠EHF = 180°
⇒ m∠E + 34° + 127° = 180°
⇒ m∠E + 161° = 180°
⇒ m∠E + 161° - 161° = 180° - 161°
⇒ m∠E = 19°
Answer:
b
Step-by-step explanation:
Heeeelppppppp meee pleeease
Answers
Step-by-step explanation:
as there are only 3 types of discontinuity overall : A, B and C.
there is no fourth, so D is out.
to check we use x = 2 in both equations and see, if and how the 2 connect or disconnect at that point.
5x + 4, x = 2
5×2 + 4 = 14
this is finite and a well-defined number.
2 - x, x = 2
2 - 2 = 0
this is again finite and well-defined.
but it is different from 14 above.
there is no multiplication factor or so that causes special values. so, there is no removable discontinuity. A is out.
none of the values at the point go to infinity, so there is no infinite discontinuity. B is out.
but yes, the functional value Suendenbock suddenly jumps at the point from 0 to 14 without any connection.
so, yes, it is a jump. C is right.
Sally had her eye on a new pair of shoes for a while. She has been waiting because, at $100, they are a little pricey for her. They are on sale now for $75. If she bought the shoes now, what percentage of the original price is she saving?
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Answer:
Price before discount: $100
Discount: 25%
Price after discount: $75
You save: $25
What are the values of y and z?
Answers
Answer:
y = 70°
z = 40°
Step-by-step explanation:
The two red marks in the sides HF and HG of the triangle means that it is an isosceles triangle, and it means that it have the two angles in the base with the same value, so the angle y have to be 70°. Now, the sum of the 3 internal angles of a triangle is always 180°. We have two angles with 70, so 70+70= 140°. 180-140 = 40°
Find the values of the variables in the figure.
Answers
Step-by-step explanation:
5y = 120
y = 24
2× = 108
x = 54
Solve the equation by completing the square.
9y2 + 12y - 11 = 0
Answers
Answer:
-⅔ +⅓ √15
Step-by-step explanation:
y= -⅔ +⅓ √15
or
y = − ⅔ + -⅓ √15
d/5 = 12/80 plz help
Answers
Answer:
= [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
naomi has earned $54 mowing lawns the past two days .She worked 2.5 hours yesterday and 4.25 hours today .if naomiis paid the same amount for every hour she works ,how much does she earn per hour to mow lawns
Answers
Answer:
8$ per hour
Step-by-step explanation
First, we need to find how many hours Naomi worked, total.
Simply add [tex]2.5+4.25=6.75[/tex]
Now we know that Naomi earned 54$ over 6.75 hours.
All we have to do to find the hourly rate is divide [tex]54/6.75=8[/tex]
Naomi earns 8$ per hour mowing lawns.
Answer:
$8
Step-by-step explanation:
Set up an equation with the payrate ($/hr) as the unknown.
2.5 × R + 4.25 × R = 54
6.75 × R = 54 ; R = [tex]\frac{54}{6.75}[/tex] = 8
What is the equation of the following Graph?
Answers
Answer:
From the shape of the graph we can state it is the transformation of the square root function:
f(x) = [tex]\sqrt{x}[/tex]This is a reflection of f(x) over x-axis, translation 3 units left and 2 units up.
The transformation is:
g(x) = - f(x + 3) + 2The equation is:
g(x) = - [tex]\sqrt{x+3} +2[/tex]Its translated square root function
y=√xRotate along x axis
y=-√xshift 3 units left
y=-√x+3shift 2 units up
y=-√(x+3)+2Millie and Molly’s ages add up to 19 years Millie is three years older than Molly how old are they
Answers
Answer:
Millie is 11. Molly is 8.
Step-by-step explanation:
Step 1: Subtract 3 from 19. The reason why you do this is to make sure that you don't have an extra 3 lying in there for the next few steps.
19-3=16
Step 2: Divide 2 from 16. You do this because there are two sisters.
16÷2=8
8 will then become Molly's age
Step 3: Add 3 to 8. This will give you Millie's age because she is 3 years older than Molly.
3+8=11
In conclusion, Millie is 11 and Molly is 8.
It’s going to be Lindsay’s birthday soon and her 5 friends Mary Jacqui Tadeusz opal and Tony have contributed equal amounts of money to buy her a present. They have $45.00 to spend between them. Determine how much each contributed
A. 5y = $45.00; y = $9.00
B. 5y = $45.00; y = $10.00
C. 5 + y = $45.00; y = $39.00
D. 5 + y = $45.00; y = $40.00
Answers
Answer:
5y = 45.00; y = $9.00
Step-by-step explanation:
What is the approximate answer
Answers
Answer:
8
Step-by-step explanation:
or 8.24
In a probability model, which of the following numbers could be the probability of an outcome?
1.5 ,1/2 ,3/4 ,2/3 ,0 ,-1/4
Answers
Answer:
Step-by-step explanation:
Don’t know
I need help again! Question below!
Answers
Answer:
20
Step-by-step explanation:
If each space has an area of 5, we just have to multiply by 4 since there are 4 spaces.
4(5)=20
Answer:
100ft²
Step-by-step explanation:
Hope this helps!
Question 2. In the given figure find the value of x in each angle of a triangle.
Very very important Plz.
Answers
Step-by-step explanation:
[tex]\sf\pink{Given}[/tex]
Angle A is ( x + 10 )Angle B is ( 3x + 5 )Angle C is ( 2x + 15 )[tex]\sf\pink{To\: Find}[/tex]
Value of "x" is ?Explanation :Rule :Sum of all angles of a triangle is 180°Therefore ,
[tex]\longrightarrow\bf{x + 10 + 3x + 5 + 2x + 15 = 180 }[/tex]
[tex]\longrightarrow\bf{x + 3x + 2x + 15 + 5 + 10 = 180 }[/tex]
[tex]\longrightarrow\bf{4x + 2x + 20 + 10 = 180 }[/tex]
[tex]\longrightarrow\bf{6x + 30 = 180 }[/tex]
[tex]\longrightarrow\bf{6x = 180 - 30 }[/tex]
[tex]\longrightarrow\bf{6x = 150 }[/tex]
[tex]\longrightarrow\bf{x = \dfrac{150}{6}}[/tex]
[tex]\longrightarrow\bf\pink{x = 25}[/tex]
Therefore value of x is 25 .
Now, finding the the measure of each angle by putting the value of "x" in their places.
∠A = (x + 10)° => (25 + 10)° => 35°
∠B = (3x + 5)° => (3×25 + 10)° => (75 + 5)° => 80°
∠C = (2x + 15)° => (2 × 25 + 10)° => (50 + 15)° => 65°
Find the measure of the angle indicated.
1029
?
A) 102°
C) 114
B) 119
D) 131°
Answers
they are alternative exterior angles. When this is the case, the angles are equal.
juan compro: 1/4 de pepino que cuesta $3, 1 1/2 de jamón que cuesta $120, 1/3 de tortillas que cuesta $6, 4/8 de queso que cuesta $45. cuanto dinero gasto en total? cuanto cuesta un kilo de queso? cuanto cuesta medio kilo de jamón? ¿Cuánto gastaría si comprara un kilo de tortilla, un kilo de pepino, y un kilo de jamón? si Juan tiene $430 que puede comprar sin que le sobre ni un peso?
Answers
En total, Juan gastó $205.25. 1 kilo de queso cuesta $90. 1/2 kilo de jamón cuesta $60. Si comprara un kilo de tortilla, un kilo de pepino y un kilo de jamón, Juan gastaría $129. Si Juan tiene $430, puede comprar 3 kilos de jamón, 1 kilo de queso, 5 kilos de pepino y 1 2/3 de tortillas.
Dado que Juan compró 1/4 de pepino que cuesta $3, 1 1/2 de jamón que cuesta $120, 1/3 de tortillas que cuesta $6 y 4/8 de queso que cuesta $45, para determinar cuánto dinero gastó en total, cuánto cuesta un kilo de queso, cuánto cuesta medio kilo de jamón, cuánto gastaría si comprara un kilo de tortilla, un kilo de pepino, y un kilo de jamón y, si Juan tiene $430, qué puede comprar sin que le sobre ni un peso, se deben realizar los siguientes cálculos:
Cuánto dinero gastó en total = valores x fracción comprada3 x 1/4 + 120 x 1 1/2 + 6 x 1/3 + 45 x 4/8 = X0.75 + 180 + 2 + 22.5 = X205.25 = XSi 4/8 de queso cuestan $45, y 4/8 es igual a 1/2, 1 kilo de queso cuesta $90 (45 x 2).Si 1 kilo de jamón cuestan $120, 1/2 kilo de jamón cuesta $60 (120 / 2).Si comprara un kilo de tortilla, un kilo de pepino y un kilo de jamón, Juan gastaría $129 (3 + 6 + 120).Si Juan tiene $430, puede comprar 3 kilos de jamón, 1 kilo de queso, 5 kilos de pepino y 1 2/3 de tortillas (120 x 3 + 45 + 3 x 5 + 6 + 6 x 0.666).Aprende más en https://brainly.com/question/15723794
Find the acute angles of a right triangle if:
A) one of them is 60 ° higher than the other;
B) one of them 2 times
C) The ratio of their values is 2:3.
help!!!!!!!!!
hurry up please and tell me about everything please
can someone help me im gonna be late pleasee do it for me my mom gonna kill me if i will got f
Answers
Answer:
A angles are 15 and 75 B. angles are 30 and 60 C. angles are 36 and 54
Step-by-step explanation:
Remember that the two acute angles of a right triangle = 90
A one angle = x ; the other angle = 60 + x so 60 +x + x = 90
60 + 2x = 90; 2x = 30; x = 15 one angles; the other angle is 60 + 15 = 75
B. One angle = x ; the other angle = 2x so x + 2x = 90
3x = 90 ; x = 30 one angle; the other angle s 2x = 2(30) = 60
C 2 : 3 means 2x:3x
One angle = 2x ; the other angle = 3x ; so 2x + 3x = 90
5x = 90; x = 18 this is what x is equal to. Now the find the angles:
one angle is 2x meaning 2(18) = 36 and the other angle is 3x meaning 3(18) = 54.
To check this answer one angle to the other angle is represented by the ratio 2:3; 36:54 = 2:3 Reduced!
What is 7054.72 rounded to the nearest 10?
Answers
Answer:
7054.7
Step-by-step explanation:
7054.7 is 7054.72 rounded to the nearst 10
Answer:
7050
Step-by-step explanation:
7050, 5 is in tens and the 4 is in ones but it's less than 5 so it will be zero
while at the beach, daniel buys lunch for his family from a food stand. he purchases one hot dog for $2.50 and 3 hamburgers. if he spent $13 total, write and solve and equation to find h, the amount each hamburger cost
Answers
Answer:
h= $3.50
Step-by-step explanation:
$2.50 + 3h = $13
3h = $13 - $2.50
h = $10.50 ÷3
h= $3.50
Write the equation of the function whose graph IS
shown.
y = ____ (x + ____)^2 + ____
Answers
Answer:
y=1(x-5)^2+3
Please correct me if i am wrong.
Step-by-step explanation:
We know that the turning point of a graph in the form a(x+p)^2+q is (-p,q) so,
TP(5,3) means that p=-5, q=3.
To solve a for the function y = a(x-5)^2+3, we can substitute one of the points we know lie on the graph for x and y so,
Substitute (8,12) into y=a(x-5)^2+3,
12=a(8-5)^2+3
12=9a+3
9=9a
a=1,
So substitute in a,
y=1(x-5)^2+3
Can some one help me
Answers
Which ones are functions?
Answers
Answer:
The first, second, third, and fourth
Step-by-step explanation:
Each input in the first, second, third, and fourth only have one output. In the fifth one 3.3 and 6.6 are seen twice as the x-value, so this is incorrect.
Cada entrada en la primera, segunda, tercera y cuarta tiene solo una salida. En el quinto, 3.3 y 6.6 se ven dos veces como el valor de x, por lo que esto es incorrecto.
Please help :(... when I posted this with 50 points someone gave me incorrect answers..
Answers
Answer:
22)43300000, 23)~7, 24)~20
Step-by-step explanation:
22)6.48*10^(7)-(2.15*10^(7))=4.33*10^7 (or 43300000)
23)2.95*10^6=2950000, 2.15*10^7=21500000, 21500000/2950000=~7
24)1.3*10^9=130000000, 1300000000/64800000=~20
Answer:
Step-by-step explanation:
22. You can write these exponents out if it makes it easier to understand, then convert back into exponential form.
6.48 x 10⁷ = 64800000 France
2.15 x 10⁷ = 21500000 Australia
Subtracting Australia from France = 43300000
Converting back to exponential would be 4.33 x 10⁷
But if you notice both number have the exponent of 10⁷. Since these are both the same, you can just subtract the whole number for Australia from the number for France 6.48 - 2.15 = 4.33
then just put the exponent on the end. 4.33 x 10⁷
23. Again it might be easier to convert to standard numbers first.
Area of Australia = 2.95 x 10⁶ or 2950000
Population = 2.15 x 10⁷ or 21500000
So population per square mile would be population divided by area.
21500000 / 2950000 = 7.3 people per square mile
Now if you look at the two numbers, the exponents are only different by 1. You can easily make the population have the same exponent as the area by moving the decimal place of the whole number
Population 2.15 x 10⁷ is the exact same as 21.5 x 10⁶. Now since both number have the same exponents, you can cancel those out and just divide the whole numbers. 21.5 divided by 2.95 which also equals 7.3.
24. You can look at this the same way.
China population 1.3 x 10⁹ is 1300000000
France population 6.48 x 10⁷ is 64800000
Dividing China by France you get about 20.1 which means China is about 20.1 times great in population than France.
If you use the same method as in question 23, you can change the population of China so the exponent matches that of France.
1.3 x 10⁹ is exactly the same as 130 x 10⁷
Again, since both exponents are the same, you can cancel them out and just divide the whole numbers.
130 / 6.48 which also equals about 20.1
please help! circled numbers only. tysm, will mark brainliest.
Answers
Answer:
10. 3/5
12. 5/6
14. 12/17
15. 2 , 5
18.7
20. 21/22
22. 15
24. 9
26.11,21
Step-by-step explanation:
Answer:
12.
[tex] \frac{5}{6} [/tex]
18. 7
24. 9
10. 3/5
16.10
22. 15
14.12/17
20.21/22
26. 11, 12
Determine the x and y intercepts of the graph of 3x + 4y = 24
Answers
Answer:
Step-by-step explanation:
3x + 4y = 24
Find the x intercept by solving intersecting the graph of f(x) or y with
y=0 (which is the x-axis)
4y= -3x+24, subtract 3x from both sides of the equation
y = (-3x/4) +6, divide both sides by 4
if y=0 then
(-3x/4) +6 = 0 , subtract 6 from both sides
-3x/4 = -6, multiply both sides by 4
-3x = -24 , divide both sides by
x= 8, so the x intercept is at (8, 0)
the general formula of a line is y=mx+b , where b is the y-intercept
since our equation is y = (-3x/4) +6 then y intercept is at (0, 6)