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Popular >

simplify (16^-)^{2/3}

Solution

simplify

(1 6^{-})^{\frac{2}{3}}

Solution

\frac{1}{4 \cdot 2 ^{\frac{2}{3}}}

+1

Decimal Notation

0.15749 \dots

Solution steps

(1 6^{-})^{\frac{2}{3}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 1 6^{- \frac{2}{3}}

Apply exponent rule:

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

= \frac{1}{1 6 ^{\frac{2}{3}}}

1 6^{\frac{2}{3}} = (2 \cdot 2^{\frac{1}{3}})^{2}

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

Apply exponent rule:

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

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

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

(2^{\frac{1}{3}})^{2} : 2^{\frac{2}{3}}

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

2^{2} = 4

= \frac{1}{4 \cdot 2 ^{\frac{2}{3}}}

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Frequently Asked Questions (FAQ)

What is (16^-)^{2/3} ?
The solution to (16^-)^{2/3} is 1/(4*2^{2/3)}