What is ((4a^3b)/(6a^5b^{-2)})^3 ?

The solution to ((4a^3b)/(6a^5b^{-2)})^3 is (8b^9)/(27a^6)

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simplify ((4a^3b)/(6a^5b^{-2)})^3

simplify

(\frac{4 a ^{3} b}{6 a ^{5} b ^{- 2}})^{3}

\frac{8 b ^{9}}{27 a ^{6}}

Solution steps

(\frac{4 a ^{3} b}{6 a ^{5} b ^{- 2}})^{3}

Apply exponent rule:

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

= \frac{( 4 a ^{3} b ) ^{3}}{( 6 a ^{5} b ^{- 2} ) ^{3}}

Simplify

(4 a^{3} b)^{3} : 64 a^{9} b^{3}

= \frac{64 a ^{9} b ^{3}}{( 6 a ^{5} b ^{- 2} ) ^{3}}

Simplify

(6 a^{5} b^{- 2})^{3} : \frac{216 a ^{15}}{b ^{6}}

= \frac{64 a ^{9} b ^{3}}{\frac{216 a ^{15}}{b ^{6}}}

Apply the fraction rule:

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

= \frac{64 a ^{9} b ^{3} b ^{6}}{216 a ^{15}}

Cancel the common factor:

8

= \frac{8 a ^{9} b ^{6} b ^{3}}{27 a ^{15}}

Apply exponent rule:

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

\frac{a ^{9}}{a ^{15}} = \frac{1}{a ^{15 - 9}}

= \frac{8 b ^{6} b ^{3}}{27 a ^{15 - 9}}

Subtract the numbers:

15 - 9 = 6

= \frac{8 b ^{6} b ^{3}}{27 a ^{6}}

8 b^{6} b^{3} = 8 b^{9}

= \frac{8 b ^{9}}{27 a ^{6}}

3 k^{4} - 48 k^{2}

125 x^{2} - 80

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

x^{2} = 400

125 + a^{3}

What is ((4a^3b)/(6a^5b^{-2)})^3 ?
The solution to ((4a^3b)/(6a^5b^{-2)})^3 is (8b^9)/(27a^6)