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

The solution to (4a^{-2}b^3)^{-3} is (a^6)/(64b^9)

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

simplify

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

\frac{a ^{6}}{64 b ^{9}}

Solution steps

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

Apply exponent rule:

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

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

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

Simplify

(4 a^{- 2} b^{3})^{3} : \frac{64 b ^{9}}{a ^{6}}

= \frac{1}{\frac{64 b ^{9}}{a ^{6}}}

Apply the fraction rule:

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

= \frac{a ^{6}}{64 b ^{9}}

(2 x + 3 y) (2 x + 3 y)

(x^{2} + 3 x - 4) + (2 x^{3} - 2 x + 5)

2 x^{3} - x^{2} - 20 x + 10

(\frac{2 ^{2}}{x})^{- 1}

\frac{2}{4} \cdot \frac{3}{6}