Question

Please help me, if you help then thanks!

Answer 1

9514 1404 393

Answer:

k = 3

Explanation:

The applicable rules of exponents are ...

(a^b)(a^c) = a^(b+c)

(a^b)^c = a^(bc)

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Using these rules, we can simplify the left-side expression, then equate exponents of the same base.

`(3)^2(3^2)^k=3^8\\\\(3^2)(3^(2k))=3^8\\\\3^(2k+2)=3^8\\\\2k+2=8\qquad\text{equate exponents}\\\\k+1=4\qquad\text{divide by 2}\\\\\boxed{k=3}\qquad\text{subtract 1}`