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Popular >

simplify (8x^6)^{(-2)/3}

Solution

simplify

(8 x^{6})^{\frac{- 2}{3}}

Solution

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

Solution steps

(8 x^{6})^{\frac{- 2}{3}}

Apply exponent rule:

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

(8 x^{6})^{\frac{- 2}{3}} = 8^{\frac{- 2}{3}} (x^{6})^{\frac{- 2}{3}}

= 8^{\frac{- 2}{3}} (x^{6})^{\frac{- 2}{3}}

8^{\frac{- 2}{3}} = \frac{1}{4}

= \frac{1}{4} (x^{6})^{\frac{- 2}{3}}

Apply exponent rule:

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

assuming

a \geq 0

(x^{6})^{\frac{- 2}{3}} = x^{6 \cdot \frac{- 2}{3}}

= \frac{1}{4} x^{6 \cdot \frac{- 2}{3}}

6 \cdot \frac{- 2}{3} = - 4

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

Apply exponent rule:

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

What is (8x^6)^{(-2)/3} ?
The solution to (8x^6)^{(-2)/3} is 1/(4x^4)