Show that: [tex]\sqrt[ab]{ \frac{ {x}^{a} }{ {x}^{b} } } . \sqrt[bc]{ \frac{ {x}^{b} }{ {x}^{c} } } . \sqrt[ca]{ \frac{ {x}^{c} }{ {x}^{a} } } = 1.[/tex]

Brainliest! Brainliest..ans.
​

Here we need to Prove that ,

[tex]\bf\implies \sqrt[ab]{ \frac{ {x}^{a} }{ {x}^{b} } } . \sqrt[bc]{ \frac{ {x}^{b} }{ {x}^{c} } } . \sqrt[ca]{ \frac{ {x}^{c} }{ {x}^{a} } } = 1.[/tex]

Lets start with LHS , which is ,

[tex]\bf\implies LHS = \sqrt[ab]{ \dfrac{ {x}^{a} }{ {x}^{b} } } . \sqrt[bc]{ \dfrac{ {x}^{b} }{ {x}^{c} } } . \sqrt[ca]{ \dfrac{ {x}^{c} }{ {x}^{a} } } [/tex]

We know that ,

[tex]\bf\implies \sqrt[n]{k^m }= k^{\frac{m}{n}}[/tex]

• So that ,

[tex]\bf\implies \sqrt[ab]{x^{a-b}} . \sqrt[bc]{x^{b-c}} .\sqrt[ac]{x^{c-a}} \\\\\bf\implies x^{\frac{a-b}{ab}} . x ^{\frac{b-c}{bc}} .x^{\frac{c-a}{ca}} \\\\\bf\implies x^{\frac{ ac - bc + ab - ac + bc - ba }{abc } }\\\\\bf\implies x^{\frac{0}{abc}} \\\\\bf\implies x^0 \\\\\bf\implies 1 = RHS [/tex]

Hence ,

[tex]\implies \boxed{\bf \red{ LHS = RHS }} [/tex]

[tex]\large\underline{\sf{Solution-}}[/tex]

Consider LHS:

[tex]\sf= \sqrt[\sf ab]{\dfrac{\sf x^{a}}{\sf x^{b}}}\cdot \sqrt[\sf bc]{\dfrac{\sf x^{b}}{\sf x^{c}}}\cdot \sqrt[\sf ac]{\dfrac{\sf x^{c}}{\sf x^{a}}}[/tex]

As we know that:

[tex]\sf\red\leadsto\dfrac{x^{a}}{x^{b}}=x^{a-b}[/tex]

We get:

[tex]\sf= \sqrt[\sf ab]{\sf x^{a-b}}\cdot \sqrt[\sf bc]{\sf x^{b-c}}\cdot \sqrt[\sf ac]{\sf x^{c-a}}[/tex]

We can also write it as:

[tex]\sf= x^{\dfrac{a-b}{ab}}\cdot x^{\dfrac{b-c}{bc}}\cdot x^{\dfrac{c-a}{ac}}[/tex]

We know that:

[tex]\sf \red\leadsto x^{a}\cdot x^{b}=x^{a+b}[/tex]

We get:

[tex]\sf= x^{\bigg(\dfrac{a-b}{ab}+\dfrac{b-c}{bc}+\dfrac{c-a}{ac}\bigg)}[/tex]

[tex]\sf= x^{\bigg(\dfrac{c(a-b)+a(b-c)+b(c-a)}{abc}\bigg)}[/tex]

[tex]\sf= x^{\bigg(\dfrac{ac-bc+ab-ac+bc-ab}{abc}\bigg)}[/tex]

[tex]\sf= x^{\bigg(\dfrac{0}{abc}\bigg)}[/tex]

[tex]\sf= x^{0}[/tex]

[tex]\sf=1[/tex]

[tex]\textsf{= RHS}\\[/tex]

1. find the measure of each angle

Express the following rate as a unit rate: 28 1/3 minutes to run 3 1/3 miles​

8x - 8 - x = 3 (6 - 2x)

Pls help I need a good grade I’ll add extra points

which of the following statements are true for sin (-430°)

i. the basic angle, a lies in the second quadrant
Ii. sin (-430°) = +sin (430°)
III. sin (-430°) = sin (70°)
iv. a = 30°​

Write the answer to 6 2/5 × 4 in improper fraction form AND mixed number form.

Improper fraction:
-------------------------

Mixed number: -------------------------
(whole number + fraction number

The equation
(p-1)x^2 + 4x + (p-5)=0, where p is a constant,
has no real roots.
(a) Show that p satisfies p^2 - 6p+1>0.

SHOW WORK. Algebra question 100 POINTS! Easy

Mrs. Gonzalez bought a puzzle for $10.95, a board game for $15.95, and a table lamp for $17.10. After tax, the total amount due was $46.86. What is the sales tax rate written as a percent? Round to the nearest tenth if necessary.

the cash cost is 4700.00 she decides to finance the project by paying 7.0% down and pays 740.00 for 6 months what is the finance charge​

<1 and <2 are complementary. Solve for the measure of <1.

<1 = 12x + 4
<2 = 9x + 2

A. 52
B. 4
C. 38
D. 8.3

Which of the following functions is graphed below?

The percent of change from 200 to 220 and indicate if it is an increase or decrease.

What two numbers multiply to 10 and add to 9

GUYS IS THIS CORRECT? CLASS 6 MATHS​

A fair die is rolled 11 times. What is the probability of rolling a 4 on the die 4 times? Express your answer as a decimal rounded to 4 decimal places after the decimal point.

What is the midpoint of the line segment from (5,-2) to (1,-5)?

If this is the graph of f(x)= a(x+h) +k, then:

If x=47 , find the measures of angles 1,2 and 3​

no links please

Suppose you took out a $120,000 loan to go to med school. Your loan has a 6.9% APR to be paid in 30 years. You make monthly payments of $790.32 – to date, you have made 180 payments. What is the total amount you have left to pay if you simply make payments for the next 180 months?​

Evaluate the solid bounded by 2x + z = 2 and (x − 1)^2 + y^2 = z. Sketch the given solid.

Evaluate v(x) = 12 - 2x - 5 when x = -2, 0, and 5

а
Mamadou has a points card for a movie theater.
• He receives 55 rewards points just for signing up.
• He earns 7-5 points for each visit to the movie theater.
• He needs at least 100 points for a free movie ticket.
.

I NEED HELP PLEASE!!!

Passing through (7,-2) and perpendicular to the line whose equation is y=1/2x+2

Point slope form=

Slope-intercept form=

Find f(0) and f(6)

f(x)= x^2+10x+72/x^2-12x+36

the correct written expression for: (9 x 5) + (24 - 9).

Balto” is a 6 year old 35 kg intact husky mix. He presents through the ER after likely being HBC (hit by car) with anisocoria and nystagmus, both signs of head trauma. The doctor instructs you to give 1 g/kg mannitol IV to decrease intracranial pressure. Mannitol is a 20 % solution. How many grams will “Balto” receive? How many mgs? How many mls?

3
Parallel to y = - -*+2 and goes through the point (5, -7)
S
please help it’s due next period

Question Choice Worth 2 points)
(02.06Derek has a bird that weighs 4 pounds. Use the double fine diagram below to help you determine approximately how many kilograms this bird weighs
3 5 7
Pounds
1 2 3
Kilograms
15 klograms
O2 xilogram
5 kilograms
7 kilograms

will mark brainlest answer the question in the picture linked below
and explain as well