Question

Determine the value of variables a, b, and c that make each equation true.

What is the value of a in this equation?

(x6 = 1

What is the value of b in this equation?

(x7) 4 = x

b=

What is the value of c in this equation?

(x2) = x 22

Answer 1

Quick Answer: A=-5 B=28 C=-11

Answer 2

Corrected Question

Determine the values of a, b and c that make each equation true.

`(x^a)^6=(1)/(x^(30)) \\\\(x^(-7))^(-4)=x^b\\\\(x^(-2))^c=x^(22)`

Answer:

a=-5, b=28 and c=-11

Explanation:

To solve for a,b and c, we apply the following laws of indices

`(1)/(x^y)=x^(-y) \\\\(x^m)^n=x^(m X n)\\\\$If x^m=x^n,$ then m=n`

Therefore

`(x^a)^6=(1)/(x^(30))\\x^(a*6)=x^(-30)\\6a=-30\\a=-5`

To solve for b

`(x^(-7))^(-4)=x^b\\x^(-7*-4)=x^b\\x^(28)=x^b\\b=28`

To solve for c

`(x^(-2))^c=x^(22)\\x^(-2*c)=x^(22)\\-2c=22\\c=-11`