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Popular >

simplify (2x^{-1})^3

Solution

simplify

(2 x^{- 1})^{3}

Solution

\frac{8}{x ^{3}}

Solution steps

(2 x^{- 1})^{3}

Apply exponent rule:

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

(2 x^{- 1})^{3} = 2^{3} (x^{- 1})^{3}

= 2^{3} (x^{- 1})^{3}

2^{3} = 8

= 8 (x^{- 1})^{3}

Apply exponent rule:

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

assuming

a \geq 0

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

= 8 x^{- 1 \cdot 3}

Multiply the numbers:

1 \cdot 3 = 3

= 8 x^{- 3}

Apply exponent rule:

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

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

= 8 \cdot \frac{1}{x ^{3}}

Simplify

8 \cdot \frac{1}{x ^{3}} : \frac{8}{x ^{3}}

= \frac{8}{x ^{3}}

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Frequently Asked Questions (FAQ)

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