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Popular >

simplify 18^{-1/2}

Solution

simplify

1 8^{- \frac{1}{2}}

Solution

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

+1

Decimal Notation

0.23570 \dots

Solution steps

1 8^{- \frac{1}{2}}

Prime factorization of

18 : 2 \cdot 3^{2}

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

Apply exponent rule:

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

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

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

Apply exponent rule:

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

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

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

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

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

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

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

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Frequently Asked Questions (FAQ)

What is 18^{-1/2} ?
The solution to 18^{-1/2} is 1/(3*2^{1/2)}