Question

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

Answer 1

Corrected Question

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

$(x^a)^6=\dfrac{1}{x^{30}} \\\\(x^{-7})^{-4}=x^b\\\\(x^{-2})^c=x^{22}$

Answer:

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

Step-by-step explanation:

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

$\dfrac{1}{x^y}=x^{-y} \\\\(x^m)^n=x^{m X n}\\\\ If x^m=x^n, then m=n$

Therefore

$(x^a)^6=\dfrac{1}{x^{30}}\\x^{a*6}=x^{-30}\\6a=-30\\a=-5$

To solve for b

$(x^{-7})^{-4}=x^b\\x^{-7*-4}=x^b\\x^{28}=x^b\\b=28$

To solve for c

$(x^{-2})^c=x^{22}\\x^{-2*c}=x^{22}\\-2c=22\\c=-11$