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

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

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

simplify

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

\frac{3}{2}

Decimal Notation

1.5

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 = - 1

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

Apply exponent rule:

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

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

= \frac{1}{\frac{2}{3}}

Apply the fraction rule:

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

= \frac{3}{2}

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