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Popular >

simplify ((1/16)^{-2/3})^{3/4}

Solution

simplify

((\frac{1}{16})^{- \frac{2}{3}})^{\frac{3}{4}}

Solution

4

Solution steps

((\frac{1}{16})^{- \frac{2}{3}})^{\frac{3}{4}}

Apply exponent rule:

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

= (\frac{1}{16})^{- \frac{2}{3} \cdot \frac{3}{4}}

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

= (\frac{1}{16})^{- \frac{1}{2}}

Apply exponent rule:

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

(\frac{1}{16})^{- \frac{1}{2}} = \frac{1}{( \frac{1}{16} ) ^{\frac{1}{2}}}

= \frac{1}{( \frac{1}{16} ) ^{\frac{1}{2}}}

(\frac{1}{16})^{\frac{1}{2}} = \frac{1}{4}

= \frac{1}{\frac{1}{4}}

\frac{1}{\frac{1}{4}} = 4

= 4

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Frequently Asked Questions (FAQ)

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