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Popular >

simplify 1/3*8^{-2/3}

Solution

simplify

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

Solution

\frac{1}{12}

+1

Decimal Notation

0.08333 \dots

Solution steps

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

Factor the number:

8 = 2^{3}

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

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

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

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

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

Apply exponent rule:

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

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

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

2^{2} = 4

= \frac{1}{3} \cdot \frac{1}{4}

\frac{1}{3} \cdot \frac{1}{4} = \frac{1}{12}

= \frac{1}{12}

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Frequently Asked Questions (FAQ)

What is 1/3*8^{-2/3} ?
The solution to 1/3*8^{-2/3} is 1/12