What is ((a^2b^{-3})/(a^{-2)b^2})^2 ?

The solution to ((a^2b^{-3})/(a^{-2)b^2})^2 is (a^8)/(b^{10)}

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simplify ((a^2b^{-3})/(a^{-2)b^2})^2

simplify

(\frac{a ^{2} b ^{- 3}}{a ^{- 2} b ^{2}})^{2}

\frac{a ^{8}}{b ^{10}}

Solution steps

(\frac{a ^{2} b ^{- 3}}{a ^{- 2} b ^{2}})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( a ^{2} b ^{- 3} ) ^{2}}{( a ^{- 2} b ^{2} ) ^{2}}

Simplify

(a^{2} b^{- 3})^{2} : \frac{a ^{4}}{b ^{6}}

= \frac{\frac{a ^{4}}{b ^{6}}}{( a ^{- 2} b ^{2} ) ^{2}}

Simplify

(a^{- 2} b^{2})^{2} : \frac{b ^{4}}{a ^{4}}

= \frac{\frac{a ^{4}}{b ^{6}}}{\frac{b ^{4}}{a ^{4}}}

Divide fractions:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{a ^{4} a ^{4}}{b ^{6} b ^{4}}

a^{4} a^{4} = a^{8}

= \frac{a ^{8}}{b ^{6} b ^{4}}

b^{6} b^{4} = b^{10}

= \frac{a ^{8}}{b ^{10}}

z^{2} + 14 z + 40 = 0

- \frac{4}{7} + \frac{2}{3}

\frac{x + 1}{2} = - 3

3 (3 - x) \geq 8 + x

y^{2} - 18 y + 81

What is ((a^2b^{-3})/(a^{-2)b^2})^2 ?
The solution to ((a^2b^{-3})/(a^{-2)b^2})^2 is (a^8)/(b^{10)}