What is [(5/2)^3]^{-4}*(4/5)^{-2} ?

The solution to [(5/2)^3]^{-4}*(4/5)^{-2} is 256/9765625

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simplify [(5/2)^3]^{-4}*(4/5)^{-2}

simplify

[(\frac{5}{2})^{3}]^{- 4} \cdot (\frac{4}{5})^{- 2}

\frac{256}{9765625}

Decimal Notation

0.0000262144

Solution steps

((\frac{5}{2})^{3})^{- 4} (\frac{4}{5})^{- 2}

((\frac{5}{2})^{3})^{- 4} = \frac{4096}{244140625}

= \frac{4096}{244140625} (\frac{4}{5})^{- 2}

Apply exponent rule:

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

(\frac{4}{5})^{- 2} = \frac{1}{( \frac{4}{5} ) ^{2}}

= \frac{4096}{244140625} \cdot \frac{1}{( \frac{4}{5} ) ^{2}}

(\frac{4}{5})^{2} = \frac{16}{25}

= \frac{4096}{244140625} \cdot \frac{1}{\frac{16}{25}}

Apply the fraction rule:

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

= \frac{4096}{244140625} \cdot \frac{25}{16}

\frac{4096}{244140625} \cdot \frac{25}{16} = \frac{256}{9765625}

= \frac{256}{9765625}

\frac{1}{3} e^{- 30}

4 π (8.85 (10)^{- 12}) (34)^{2} (\frac{1}{100})^{2}

10 e^{- \frac{1}{( 108 \cdot 0.01 )}}

What is [(5/2)^3]^{-4}*(4/5)^{-2} ?
The solution to [(5/2)^3]^{-4}*(4/5)^{-2} is 256/9765625