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Popular >

simplify (9x^{-5})^3

Solution

simplify

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

Solution

\frac{729}{x ^{15}}

Solution steps

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

Apply exponent rule:

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

(9 x^{- 5})^{3} = 9^{3} (x^{- 5})^{3}

= 9^{3} (x^{- 5})^{3}

9^{3} = 729

= 729 (x^{- 5})^{3}

Apply exponent rule:

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

assuming

a \geq 0

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

= 729 x^{- 5 \cdot 3}

Multiply the numbers:

5 \cdot 3 = 15

= 729 x^{- 15}

Apply exponent rule:

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

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

= 729 \cdot \frac{1}{x ^{15}}

Simplify

729 \cdot \frac{1}{x ^{15}} : \frac{729}{x ^{15}}

= \frac{729}{x ^{15}}

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Frequently Asked Questions (FAQ)

What is (9x^{-5})^3 ?
The solution to (9x^{-5})^3 is (729)/(x^{15)}