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Popular >

simplify (-27x^{-9})^{1/3}

Solution

simplify

(- 27 x^{- 9})^{\frac{1}{3}}

Solution

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

Solution steps

(- 27 x^{- 9})^{\frac{1}{3}}

Apply exponent rule:

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

if

n

is odd

(- 27 x^{- 9})^{\frac{1}{3}} = - (27 x^{- 9})^{\frac{1}{3}}

= - (27 x^{- 9})^{\frac{1}{3}}

Apply exponent rule:

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

(27 x^{- 9})^{\frac{1}{3}} = 2 7^{\frac{1}{3}} (x^{- 9})^{\frac{1}{3}}

= - 2 7^{\frac{1}{3}} (x^{- 9})^{\frac{1}{3}}

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

= - 3 (x^{- 9})^{\frac{1}{3}}

Apply exponent rule:

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

assuming

a \geq 0

(x^{- 9})^{\frac{1}{3}} = x^{- 9 \cdot \frac{1}{3}}

= - 3 x^{- 9 \cdot \frac{1}{3}}

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

= - 3 x^{- 3}

Apply exponent rule:

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

What is (-27x^{-9})^{1/3} ?
The solution to (-27x^{-9})^{1/3} is -3/(x^3)