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Popular >

simplify 8^{-3/2}

Solution

simplify

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

Solution

\frac{1}{16 \cdot 2 ^{\frac{1}{2}}}

+1

Decimal Notation

0.04419 \dots

Solution steps

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

Prime factorization of

8 : 2^{3}

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

Apply exponent rule:

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

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

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

Apply exponent rule:

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

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

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

(2^{2})^{- \frac{3}{2}} = \frac{1}{8}

= \frac{1}{8} \cdot 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}{8} \cdot \frac{1}{2 ^{\frac{3}{2}}}

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

= \frac{1}{8} \cdot \frac{1}{2 \cdot 2 ^{\frac{1}{2}}}

\frac{1}{8} \cdot \frac{1}{2 \cdot 2 ^{\frac{1}{2}}} = \frac{1}{16 \cdot 2 ^{\frac{1}{2}}}

= \frac{1}{16 \cdot 2 ^{\frac{1}{2}}}

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Frequently Asked Questions (FAQ)

What is 8^{-3/2} ?
The solution to 8^{-3/2} is 1/(16*2^{1/2)}