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Popular >

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

Solution

simplify

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

Solution

\frac{27}{x ^{6}}

Solution steps

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

Apply exponent rule:

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

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

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

3^{3} = 27

= 27 (x^{- 2})^{3}

Apply exponent rule:

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

assuming

a \geq 0

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

= 27 x^{- 2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= 27 x^{- 6}

Apply exponent rule:

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

x^{- 6} = \frac{1}{x ^{6}}

= 27 \cdot \frac{1}{x ^{6}}

Simplify

27 \cdot \frac{1}{x ^{6}} : \frac{27}{x ^{6}}

= \frac{27}{x ^{6}}

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Frequently Asked Questions (FAQ)

What is (3x^{-2})^3 ?
The solution to (3x^{-2})^3 is (27)/(x^6)