Chapter 3 - Exponents, Polynomials and Functions - 3.1 Rules for Exponents - 3.1 Exercises - Page 233: 30

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

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}