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

The solution to (2/a)^3((4b^3)/(3a))^{-4} is (81a)/(32b^{12)}

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

simplify

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

\frac{81 a}{32 b ^{12}}

Solution steps

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

Simplify

(\frac{2}{a})^{3} : \frac{8}{a ^{3}}

= \frac{8}{a ^{3}} (\frac{4 b ^{3}}{3 a})^{- 4}

Simplify

(\frac{4 b ^{3}}{3 a})^{- 4} : \frac{81 a ^{4}}{256 b ^{12}}

= \frac{8}{a ^{3}} \cdot \frac{81 a ^{4}}{256 b ^{12}}

Apply the fraction rule:

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

= \frac{8 \cdot 81 a ^{4}}{a ^{3} \cdot 256 b ^{12}}

Factor the number:

256 = 8 \cdot 32

= \frac{8 \cdot 81 a ^{4}}{a ^{3} \cdot 8 \cdot 32 b ^{12}}

Cancel the common factor:

8

= \frac{81 a ^{4}}{a ^{3} \cdot 32 b ^{12}}

Simplify

\frac{a ^{4}}{a ^{3}} : a

= \frac{81 a}{32 b ^{12}}

\frac{- 3 x}{x}

\frac{x - c}{a + b} + \frac{x - b}{a + c} + \frac{x - a}{b + c}

(\frac{1}{3} - 6 m) - (\frac{1}{4} n - 8)

\frac{7 !}{( 7 - 2 ) !}

1 - \frac{1}{x + 1}

What is (2/a)^3((4b^3)/(3a))^{-4} ?
The solution to (2/a)^3((4b^3)/(3a))^{-4} is (81a)/(32b^{12)}