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
• c=-11

Step-by-step explanation:

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

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

Therefore :

Part 1

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

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

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