#### Answer

Simplifying the expression $5^{-2}$ to $\dfrac{1}{-25}$ was the source of error.
The correct answer is $\dfrac{a^3}{25b^{6}}.$

#### Work Step by Step

Using the Negative Exponent Rule of the laws of exponents, which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression, $5^{-2}a^3b^{-6},$ is equivalent to
\begin{array}{l}\require{cancel}
5^{-2}a^3b^{-6}
\\\\=
\dfrac{a^3}{5^{2}b^{6}}
\\\\=
\dfrac{a^3}{25b^{6}}
.\end{array}