What is factor (2c^4d^{-2})^{-3} ?

The solution to factor (2c^4d^{-2})^{-3} is (d^6)/(8c^{12)}

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factor (2c^4d^{-2})^{-3}

factor

(2 c^{4} d^{- 2})^{- 3}

\frac{d ^{6}}{8 c ^{12}}

Solution steps

(2 c^{4} d^{- 2})^{- 3}

Multiply

2 c^{4} d^{- 2} : \frac{2 c ^{4}}{d ^{2}}

= (\frac{2 c ^{4}}{d ^{2}})^{- 3}

Apply exponent rule:

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

= \frac{1}{( \frac{2 c ^{4}}{d ^{2}} ) ^{3}}

Apply exponent rule:

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

(\frac{2 c ^{4}}{d ^{2}})^{3} = \frac{( 2 c ^{4} ) ^{3}}{( d ^{2} ) ^{3}}

= \frac{1}{\frac{( 2 c ^{4} ) ^{3}}{( d ^{2} ) ^{3}}}

(d^{2})^{3} : d^{6}

= \frac{1}{\frac{( 2 c ^{4} ) ^{3}}{d ^{6}}}

Apply exponent rule:

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

(2 c^{4})^{3} = 2^{3} (c^{4})^{3}

= \frac{1}{\frac{2 ^{3} ( c ^{4} ) ^{3}}{d ^{6}}}

(c^{4})^{3} : c^{12}

= \frac{1}{\frac{2 ^{3} c ^{12}}{d ^{6}}}

Apply the fraction rule:

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

= \frac{d ^{6}}{2 ^{3} c ^{12}}

2^{3} = 8

= \frac{d ^{6}}{8 c ^{12}}

- \frac{π}{2} < x < \frac{π}{2}

0.1

\frac{x ^{- 3}}{y ^{- 2}}

7 > \frac{w}{5} - 8

\frac{x ^{2} - x - 12}{x ^{2} + x - 6} > 0

What is factor (2c^4d^{-2})^{-3} ?
The solution to factor (2c^4d^{-2})^{-3} is (d^6)/(8c^{12)}