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

The solution to ((2ab)^3)/((2a^{-2)b^2)^2} is (2a^7)/b

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

simplify

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

\frac{2 a ^{7}}{b}

Solution steps

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(2 ab)^{3} = 2^{3} a^{3} b^{3}

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

Simplify

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

= \frac{2 ^{3} a ^{3} b ^{3}}{2 ^{2} \cdot \frac{1}{a ^{4}} b ^{4}}

\frac{2 ^{3}}{2 ^{2}} = 2

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

Simplify

\frac{b ^{3}}{b ^{4}} : \frac{1}{b}

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

Simplify

\frac{2 a ^{3}}{\frac{1}{a ^{4}} b} : \frac{2 a ^{7}}{b}

= \frac{2 a ^{7}}{b}

\frac{10}{- \frac{5}{8}}

x^{2} - 4 x - 1 = 0

0.6 x^{2} - 2.4 x - 0.6 = 0

\frac{x ^{- 6}}{x ^{- 4}}

0 = x^{2} - 41 x + 238

What is ((2ab)^3)/((2a^{-2)b^2)^2} ?
The solution to ((2ab)^3)/((2a^{-2)b^2)^2} is (2a^7)/b