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Popular >

simplify (-125x^{-6})^{1/3}

Solution

simplify

(- 125 x^{- 6})^{\frac{1}{3}}

Solution

- \frac{5}{x ^{2}}

Solution steps

(- 125 x^{- 6})^{\frac{1}{3}}

Apply exponent rule:

(- a)^{\frac{1}{n}} = - (a)^{\frac{1}{n}},

if

n

is odd

(- 125 x^{- 6})^{\frac{1}{3}} = - (125 x^{- 6})^{\frac{1}{3}}

= - (125 x^{- 6})^{\frac{1}{3}}

Apply exponent rule:

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

(125 x^{- 6})^{\frac{1}{3}} = 12 5^{\frac{1}{3}} (x^{- 6})^{\frac{1}{3}}

= - 12 5^{\frac{1}{3}} (x^{- 6})^{\frac{1}{3}}

12 5^{\frac{1}{3}} = 5

= - 5 (x^{- 6})^{\frac{1}{3}}

Apply exponent rule:

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

assuming

a \geq 0

(x^{- 6})^{\frac{1}{3}} = x^{- 6 \cdot \frac{1}{3}}

= - 5 x^{- 6 \cdot \frac{1}{3}}

- 6 \cdot \frac{1}{3} = - 2

= - 5 x^{- 2}

Apply exponent rule:

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

x^{- 2} = \frac{1}{x ^{2}}

= - 5 \cdot \frac{1}{x ^{2}}

Simplify

5 \cdot \frac{1}{x ^{2}} : \frac{5}{x ^{2}}

= - \frac{5}{x ^{2}}

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Frequently Asked Questions (FAQ)

What is (-125x^{-6})^{1/3} ?
The solution to (-125x^{-6})^{1/3} is -5/(x^2)