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

Exercise

Simplify the expression:

(a5b3)4(a4)2(a2)6b3b9\frac{{(a^{-5} b^3)}^{-4}\cdot {(a^4)}^{-2}}{{(a^{-2})}^{-6}\cdot b^{-3}\cdot b^{-9}}

Final Answer

(a5b3)4(a4)2(a2)6b3b9=1\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:

(a5b3)4(a4)2(a2)6b3b9=\frac{{(a^{-5} b^3)}^{-4}\cdot {(a^4)}^{-2}}{{(a^{-2})}^{-6}\cdot b^{-3}\cdot b^{-9}}=

=a20b12a8a12b12==\frac{a^{20}\cdot b^{-12}\cdot a^{-8}}{a^{12}\cdot b^{-12}}=

=a12b12a12b12==\frac{a^{12}\cdot b^{-12}}{a^{12}\cdot b^{-12}}=

=1=1

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