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Popular >

simplify (-343x^{-12})^{1/3}

Solution

simplify

(- 343 x^{- 12})^{\frac{1}{3}}

Solution

- \frac{7}{x ^{4}}

Solution steps

(- 343 x^{- 12})^{\frac{1}{3}}

Apply exponent rule:

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

if

n

is odd

(- 343 x^{- 12})^{\frac{1}{3}} = - (343 x^{- 12})^{\frac{1}{3}}

= - (343 x^{- 12})^{\frac{1}{3}}

Apply exponent rule:

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

(343 x^{- 12})^{\frac{1}{3}} = 34 3^{\frac{1}{3}} (x^{- 12})^{\frac{1}{3}}

= - 34 3^{\frac{1}{3}} (x^{- 12})^{\frac{1}{3}}

34 3^{\frac{1}{3}} = 7

= - 7 (x^{- 12})^{\frac{1}{3}}

Apply exponent rule:

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

assuming

a \geq 0

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

= - 7 x^{- 12 \cdot \frac{1}{3}}

- 12 \cdot \frac{1}{3} = - 4

= - 7 x^{- 4}

Apply exponent rule:

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

x^{- 4} = \frac{1}{x ^{4}}

= - 7 \cdot \frac{1}{x ^{4}}

Simplify

7 \cdot \frac{1}{x ^{4}} : \frac{7}{x ^{4}}

= - \frac{7}{x ^{4}}

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Frequently Asked Questions (FAQ)

What is (-343x^{-12})^{1/3} ?
The solution to (-343x^{-12})^{1/3} is -7/(x^4)