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Popular >

simplify 1/2 9^{-1/2}

Solution

simplify

\frac{1}{2} 9^{- \frac{1}{2}}

Solution

\frac{1}{6}

+1

Decimal Notation

0.16666 \dots

Solution steps

\frac{1}{2} \cdot 9^{- \frac{1}{2}}

Factor the number:

9 = 3^{2}

= \frac{1}{2} (3^{2})^{- \frac{1}{2}}

Apply exponent rule:

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

(3^{2})^{- \frac{1}{2}} = 3^{2 (- \frac{1}{2})}

= \frac{1}{2} \cdot 3^{2 (- \frac{1}{2})}

2 (- \frac{1}{2}) = - 1

= \frac{1}{2} \cdot 3^{- 1}

Apply exponent rule:

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

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

= \frac{1}{2} \cdot \frac{1}{3}

\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}

= \frac{1}{6}

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Frequently Asked Questions (FAQ)

What is 1/2 9^{-1/2} ?
The solution to 1/2 9^{-1/2} is 1/6