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

The solution to ((2a^{-1}b)/(a^2b^{-3)})^{-2} is (a^6)/(4b^8)

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

simplify

(\frac{2 a ^{- 1} b}{a ^{2} b ^{- 3}})^{- 2}

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

Solution steps

(\frac{2 a ^{- 1} b}{a ^{2} b ^{- 3}})^{- 2}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

(\frac{2 a ^{- 1} b}{a ^{2} b ^{- 3}})^{- 2} = \frac{1}{( \frac{2 a ^{- 1} b}{a ^{2} b ^{- 3}} ) ^{2}}

= \frac{1}{( \frac{2 a ^{- 1} b}{a ^{2} b ^{- 3}} ) ^{2}}

Simplify

(\frac{2 a ^{- 1} b}{a ^{2} b ^{- 3}})^{2} : \frac{4 b ^{8}}{a ^{6}}

= \frac{1}{\frac{4 b ^{8}}{a ^{6}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

- \frac{2}{3}

0.5 a c + 0.5 c b

- 6 x - 1 < \frac{3 x - 4}{- 1} \leq 2 + x

4 y - 8 = 24

8 x^{5} y^{2} - 27 x^{2} y^{5}

What is ((2a^{-1}b)/(a^2b^{-3)})^{-2} ?
The solution to ((2a^{-1}b)/(a^2b^{-3)})^{-2} is (a^6)/(4b^8)