College Algebra (10th Edition)

$\dfrac{1}{4}$
RECALL: (1) $a^{-m} = \dfrac{1}{a^m}$ (2) $a^{mn}= (a^m)^n$ Note that $2x=-x(-2)$ Thus, $3^{2x} = 3^{-x(-2)}$ Use rule (2) above to obtain: $3^{-x(-2)} = (3^{-x})^{-2}$ With $3^{-x} = 2$, the expression above is equivalent to: $(3^{-x})^{-2} = 2^{-2}$ Use rule (1) above to obtain: $2^{-2} = \dfrac{1}{2^2} = \dfrac{1}{4}$ Thus, $3^{2x} = \dfrac{1}{4}$