simplify 2^{(-3)/2}

Solution

simplify

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

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

Decimal Notation

0.35355 \dots

Solution steps

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

Apply the fraction rule:

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

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

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

Apply exponent rule:

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

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

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

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

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

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