What is 16*(2/3)^{-4} ?

The solution to 16*(2/3)^{-4} is 81

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

simplify

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

81

Solution steps

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

Apply exponent rule:

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

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

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

(\frac{2}{3})^{4} = \frac{16}{81}

= 16 \cdot \frac{1}{\frac{16}{81}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= 16 \cdot \frac{81}{16}

Convert element to fraction:

16 = \frac{16}{1}

= \frac{16}{1} \cdot \frac{81}{16}

Cross-cancel common factor:

16

= \frac{81}{1}

Divide the numbers:

\frac{81}{1} = 81

= 81

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