9514 1404 393
Answer:
k = 3
Step-by-step 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.
[tex](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}[/tex]
