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Popular >

simplify (32/5)^{-2x}

Solution

simplify

(\frac{32}{5})^{- 2 x}

Solution

(\frac{5}{32})^{2 x}

Solution steps

(\frac{32}{5})^{- 2 x}

Apply exponent rule:

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

(\frac{32}{5})^{- 2 x} = \frac{1}{( \frac{32}{5} ) ^{2 x}}

= \frac{1}{( \frac{32}{5} ) ^{2 x}}

(\frac{32}{5})^{2 x} = \frac{3 2 ^{2 x}}{5 ^{2 x}}

= \frac{1}{\frac{3 2 ^{2 x}}{5 ^{2 x}}}

Apply the fraction rule:

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

= \frac{5 ^{2 x}}{3 2 ^{2 x}}

Apply exponent rule:

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

= (\frac{5}{32})^{2 x}

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Frequently Asked Questions (FAQ)

What is (32/5)^{-2x} ?
The solution to (32/5)^{-2x} is (5/32)^{2x}