What is (a^4b^{-1})^{-2}(a^{-3}b)^2 ?

The solution to (a^4b^{-1})^{-2}(a^{-3}b)^2 is (b^4)/(a^{14)}

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simplify (a^4b^{-1})^{-2}(a^{-3}b)^2

simplify

(a^{4} b^{- 1})^{- 2} (a^{- 3} b)^{2}

\frac{b ^{4}}{a ^{14}}

Solution steps

(a^{4} b^{- 1})^{- 2} (a^{- 3} b)^{2}

Simplify

(a^{4} b^{- 1})^{- 2} : \frac{b ^{2}}{a ^{8}}

= \frac{b ^{2}}{a ^{8}} (a^{- 3} b)^{2}

Simplify

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

= \frac{b ^{2}}{a ^{8}} \cdot \frac{b ^{2}}{a ^{6}}

Apply the fraction rule:

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

= \frac{b ^{2} b ^{2}}{a ^{8} a ^{6}}

Simplify

b^{2} b^{2} : b^{4}

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

Simplify

a^{8} a^{6} : a^{14}

= \frac{b ^{4}}{a ^{14}}

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\frac{( 2 x + 4 )}{( 2 x - 4 )}

\frac{( 17 x ^{6} - x ^{6} )}{( 2 x ^{3} ) - ( 2 x ) ^{2} \cdot 2 x}

What is (a^4b^{-1})^{-2}(a^{-3}b)^2 ?
The solution to (a^4b^{-1})^{-2}(a^{-3}b)^2 is (b^4)/(a^{14)}