Question

5^x=\sqrt[3]{25}\cdot 125^{-2}

Answer 1

[AI-generated answer — Bot]

Rewriting $\sqrt[3]{25}$ and $125^{-2}$ using exponents, we have $5^{\frac{3}{2}}$ and $5^{-6}$, respectively. This gives \begin{align*}

5^x&=5^{\frac{3}{2}}\cdot 5^{-6}\\
\Rightarrow\qquad 5^x&=5^{\frac{3}{2}-6}\\
\Rightarrow\qquad 5^x&=5^{-\frac{9}{2}}.
\end{align*}Therefore, $x=-\frac{9}{2}$ and our final answer is $\boxed{-\frac{9}{2}}$.