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Popular >

simplify 9^{(-5)/2}

Solution

simplify

9^{\frac{- 5}{2}}

Solution

\frac{1}{243}

+1

Solution steps

9^{\frac{- 5}{2}}

Factor the number:

9 = 3^{2}

= (3^{2})^{\frac{- 5}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 3^{2 \cdot \frac{- 5}{2}}

2 \cdot \frac{- 5}{2} = - 5

= 3^{- 5}

Apply exponent rule:

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

3^{- 5} = \frac{1}{3 ^{5}}

= \frac{1}{3 ^{5}}

3^{5} = 243

= \frac{1}{243}

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Frequently Asked Questions (FAQ)

What is 9^{(-5)/2} ?
The solution to 9^{(-5)/2} is 1/243