Corrected Question
Determine the values of a, b and c that make each equation true.
[tex](x^a)^6=\dfrac{1}{x^{30}} \\\\(x^{-7})^{-4}=x^b\\\\(x^{-2})^c=x^{22}[/tex]
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
[tex]\dfrac{1}{x^y}=x^{-y} \\\\(x^m)^n=x^{m X n}\\\\$If x^m=x^n,$ then m=n[/tex]
Therefore
[tex](x^a)^6=\dfrac{1}{x^{30}}\\x^{a*6}=x^{-30}\\6a=-30\\a=-5[/tex]
To solve for b
[tex](x^{-7})^{-4}=x^b\\x^{-7*-4}=x^b\\x^{28}=x^b\\b=28[/tex]
To solve for c
[tex](x^{-2})^c=x^{22}\\x^{-2*c}=x^{22}\\-2c=22\\c=-11[/tex]
