What is ((16c^6c^{-2})/((2c^2)^3))^{-1} ?

The solution to ((16c^6c^{-2})/((2c^2)^3))^{-1} is (c^2)/2

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simplify ((16c^6c^{-2})/((2c^2)^3))^{-1}

simplify

(\frac{16 c ^{6} c ^{- 2}}{( 2 c ^{2} ) ^{3}})^{- 1}

\frac{c ^{2}}{2}

Solution steps

(\frac{16 c ^{6} c ^{- 2}}{( 2 c ^{2} ) ^{3}})^{- 1}

Apply exponent rule:

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

(\frac{16 c ^{6} c ^{- 2}}{( 2 c ^{2} ) ^{3}})^{- 1} = \frac{1}{\frac{16 c ^{6} c ^{- 2}}{( 2 c ^{2} ) ^{3}}}

= \frac{1}{\frac{16 c ^{6} c ^{- 2}}{( 2 c ^{2} ) ^{3}}}

\frac{16 c ^{6} c ^{- 2}}{( 2 c ^{2} ) ^{3}} = \frac{16 c ^{4}}{( 2 c ^{2} ) ^{3}}

= \frac{1}{\frac{16 c ^{4}}{( 2 c ^{2} ) ^{3}}}

Apply the fraction rule:

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

= \frac{( 2 c ^{2} ) ^{3}}{16 c ^{4}}

Factor

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

Factor

16 : 2^{4}

= \frac{2 ^{3} c ^{6}}{2 ^{4} c ^{4}}

Cancel

\frac{2 ^{3} c ^{6}}{2 ^{4} c ^{4}} : \frac{c ^{2}}{2}

= \frac{c ^{2}}{2}

- 7 w + 6 = - 4 w^{2}

20 a = 400

x^{2 - 16}

- 5 \leq \frac{x - 2}{- 3} < 3

\frac{5}{4} x + \frac{1}{2} = x - \frac{1}{2}

What is ((16c^6c^{-2})/((2c^2)^3))^{-1} ?
The solution to ((16c^6c^{-2})/((2c^2)^3))^{-1} is (c^2)/2