Question

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

What is the value of a in this equation?

(x936 = 1

30

a=

What is the value of b in this equation?

(x-7) -4 = x

b =

What is the value of c in this equation?

(x2) c = 222

C =

Answer 1

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
• c=-11

Explanation:

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

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

Therefore :

Part 1

`(x^a)^6=(1)/(x^(30))\\\\x^(a*6)=x^(-30)\\6a=-30\\$Divide both sides by 6\\a=-5`

Part 2

To solve for b

`(x^(-7))^(-4)=x^b\\x^(-7*-4)=x^b\\x^(28)=x^b\\$Since they have the same base\\b=28`

Part 3

To solve for c

`(x^(-2))^c=x^(22)\\x^(-2*c)=x^(22)\\$Just as in part 2, the two sides of the equality have the same base, therefore:\\-2c=22\\Divide both sides by -2\\c=-11`