What is (27x^{-3})^{1/3} ?

The solution to (27x^{-3})^{1/3} is 3/x

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simplify (27x^{-3})^{1/3}

simplify

(27 x^{- 3})^{\frac{1}{3}}

\frac{3}{x}

Solution steps

(27 x^{- 3})^{\frac{1}{3}}

Apply exponent rule:

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

(27 x^{- 3})^{\frac{1}{3}} = 2 7^{\frac{1}{3}} (x^{- 3})^{\frac{1}{3}}

= 2 7^{\frac{1}{3}} (x^{- 3})^{\frac{1}{3}}

2 7^{\frac{1}{3}} = 3

= 3 (x^{- 3})^{\frac{1}{3}}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

(x^{- 3})^{\frac{1}{3}} = x^{- 3 \cdot \frac{1}{3}}

= 3 x^{- 3 \cdot \frac{1}{3}}

- 3 \cdot \frac{1}{3} = - 1

= 3 x^{- 1}

Apply exponent rule:

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

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

= 3 \cdot \frac{1}{x}

Simplify

3 \cdot \frac{1}{x} : \frac{3}{x}

= \frac{3}{x}

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