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Popular >

simplify (32)^{-1/2}

Solution

simplify

(32)^{- \frac{1}{2}}

Solution

\frac{1}{4 \cdot 2 ^{\frac{1}{2}}}

+1

Decimal Notation

0.17677 \dots

Solution steps

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

Prime factorization of

32 : 2^{5}

= (2^{5})^{- \frac{1}{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

2^{5} = 2^{4} \cdot 2

= (2^{4} \cdot 2)^{- \frac{1}{2}}

Apply exponent rule:

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

(2^{4} \cdot 2)^{- \frac{1}{2}} = (2^{4})^{- \frac{1}{2}} \cdot 2^{- \frac{1}{2}}

= (2^{4})^{- \frac{1}{2}} \cdot 2^{- \frac{1}{2}}

(2^{4})^{- \frac{1}{2}} = \frac{1}{4}

= \frac{1}{4} \cdot 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}{4} \cdot \frac{1}{2 ^{\frac{1}{2}}}

\frac{1}{4} \cdot \frac{1}{2 ^{\frac{1}{2}}} = \frac{1}{4 \cdot 2 ^{\frac{1}{2}}}

= \frac{1}{4 \cdot 2 ^{\frac{1}{2}}}

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Frequently Asked Questions (FAQ)

What is (32)^{-1/2} ?
The solution to (32)^{-1/2} is 1/(4*2^{1/2)}