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Solve: $(a^{-7}b^{-2})^{-9}=?$

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Multiplication with rational exponents

Full solution

Q. Solve:

(a^{-7}b^{-2})^{-9}=?

Apply Power Rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(x^m)^n = x^{(m*n)}$ . We will apply this rule to both $a^{(-7)}$ and $b^{(-2)}$ with the outer exponent of $-9$ . $\newline$ $(a^{(-7)})^{(-9)} * (b^{(-2)})^{(-9)}$
Multiply Exponents: Multiply the exponents. $\newline$ Now we multiply the exponents inside the parentheses by the exponent outside. $\newline$ $a^{(-7)(-9)} \times b^{(-2)(-9)}$
Perform Multiplication: Perform the multiplication. $\newline$ Calculate the products of the exponents. $\newline$ $a^{63} \times b^{18}$
Write Final Expression: Write the final simplified expression. $\newline$ The expression is now simplified to a product of two terms with positive exponents. $\newline$ $a^{63} \cdot b^{18}$

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