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Powers and Roots – Simplify an expression with powers – Exercise 5564

Exercise

Simplify the expression:

\frac{{(a^{-5} b^3)}^{-4}\cdot {(a^4)}^{-2}}{{(a^{-2})}^{-6}\cdot b^{-3}\cdot b^{-9}}

Final Answer

\frac{{(a^{-5} b^3)}^{-4}\cdot {(a^4)}^{-2}}{{(a^{-2})}^{-6}\cdot b^{-3}\cdot b^{-9}}=1

Solution

Using Powers and Roots rules we get:

\frac{{(a^{-5} b^3)}^{-4}\cdot {(a^4)}^{-2}}{{(a^{-2})}^{-6}\cdot b^{-3}\cdot b^{-9}}=

=\frac{a^{20}\cdot b^{-12}\cdot a^{-8}}{a^{12}\cdot b^{-12}}=

=\frac{a^{12}\cdot b^{-12}}{a^{12}\cdot b^{-12}}=

=1

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