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

The solution to (2/3)^{-2}*(2/3)^{-3} is 243/32

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

simplify

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

\frac{243}{32}

Decimal Notation

7.59375

Solution steps

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

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

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

Subtract the numbers:

- 2 - 3 = - 5

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

Apply exponent rule:

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

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

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

(\frac{2}{3})^{5} = \frac{32}{243}

= \frac{1}{\frac{32}{243}}

Apply the fraction rule:

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

= \frac{243}{32}

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