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Popular >

simplify (-243x^{-15})^{1/5}

Solution

simplify

(- 243 x^{- 15})^{\frac{1}{5}}

Solution

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

Solution steps

(- 243 x^{- 15})^{\frac{1}{5}}

Apply exponent rule:

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

if

n

is odd

(- 243 x^{- 15})^{\frac{1}{5}} = - (243 x^{- 15})^{\frac{1}{5}}

= - (243 x^{- 15})^{\frac{1}{5}}

Apply exponent rule:

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

(243 x^{- 15})^{\frac{1}{5}} = 24 3^{\frac{1}{5}} (x^{- 15})^{\frac{1}{5}}

= - 24 3^{\frac{1}{5}} (x^{- 15})^{\frac{1}{5}}

24 3^{\frac{1}{5}} = 3

= - 3 (x^{- 15})^{\frac{1}{5}}

Apply exponent rule:

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

assuming

a \geq 0

(x^{- 15})^{\frac{1}{5}} = x^{- 15 \cdot \frac{1}{5}}

= - 3 x^{- 15 \cdot \frac{1}{5}}

- 15 \cdot \frac{1}{5} = - 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 (-243x^{-15})^{1/5} ?
The solution to (-243x^{-15})^{1/5} is -3/(x^3)