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

The solution to ((2^3)/3)^5*((3^2)/(2^5))^{-2} is 33554432/19683

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

simplify

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

\frac{33554432}{19683}

Decimal Notation

1704.74175 \dots

Solution steps

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

(\frac{2 ^{3}}{3})^{5} = \frac{32768}{243}

= \frac{32768}{243} (\frac{3 ^{2}}{2 ^{5}})^{- 2}

Apply exponent rule:

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

(\frac{3 ^{2}}{2 ^{5}})^{- 2} = \frac{1}{( \frac{3 ^{2}}{2 ^{5}} ) ^{2}}

= \frac{32768}{243} \cdot \frac{1}{( \frac{3 ^{2}}{2 ^{5}} ) ^{2}}

(\frac{3 ^{2}}{2 ^{5}})^{2} = \frac{81}{1024}

= \frac{32768}{243} \cdot \frac{1}{\frac{81}{1024}}

Apply the fraction rule:

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

= \frac{32768}{243} \cdot \frac{1024}{81}

\frac{32768}{243} \cdot \frac{1024}{81} = \frac{33554432}{19683}

= \frac{33554432}{19683}

19.777 \cdot e^{(- 0.00226 \cdot 10)}

e^{- 0.49}

(\frac{55.34}{5}) (\frac{40.84}{5})

What is ((2^3)/3)^5*((3^2)/(2^5))^{-2} ?
The solution to ((2^3)/3)^5*((3^2)/(2^5))^{-2} is 33554432/19683