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Popular >

simplify (-3x^{-5})^3

Solution

simplify

(- 3 x^{- 5})^{3}

Solution

- \frac{27}{x ^{15}}

Solution steps

(- 3 x^{- 5})^{3}

Apply exponent rule:

(- a)^{n} = - a^{n},

if

n

is odd

(- 3 x^{- 5})^{3} = - (3 x^{- 5})^{3}

= - (3 x^{- 5})^{3}

Apply exponent rule:

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

(3 x^{- 5})^{3} = 3^{3} (x^{- 5})^{3}

= - 3^{3} (x^{- 5})^{3}

3^{3} = 27

= - 27 (x^{- 5})^{3}

Apply exponent rule:

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

assuming

a \geq 0

(x^{- 5})^{3} = x^{- 5 \cdot 3}

= - 27 x^{- 5 \cdot 3}

Multiply the numbers:

5 \cdot 3 = 15

= - 27 x^{- 15}

Apply exponent rule:

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

x^{- 15} = \frac{1}{x ^{15}}

= - 27 \cdot \frac{1}{x ^{15}}

Simplify

27 \cdot \frac{1}{x ^{15}} : \frac{27}{x ^{15}}

= - \frac{27}{x ^{15}}

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Frequently Asked Questions (FAQ)

What is (-3x^{-5})^3 ?
The solution to (-3x^{-5})^3 is -(27)/(x^{15)}