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Popular >

simplify 27^{-1/2}

Solution

simplify

2 7^{- \frac{1}{2}}

Solution

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

+1

Decimal Notation

0.19245 \dots

Solution steps

2 7^{- \frac{1}{2}}

Prime factorization of

27 : 3^{3}

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

Apply exponent rule:

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

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

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

Apply exponent rule:

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

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

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

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

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

Apply exponent rule:

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

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

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

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

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

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Frequently Asked Questions (FAQ)

What is 27^{-1/2} ?
The solution to 27^{-1/2} is 1/(3*3^{1/2)}