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

The solution to (2^{-3}*3^2)^2 is 81/64

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

simplify

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

\frac{81}{64}

Decimal Notation

1.265625

Solution steps

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

(2^{- 3})^{2} = \frac{1}{64}

= \frac{1}{64} (3^{2})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

(3^{2})^{2} = 3^{2 \cdot 2}

= \frac{1}{64} \cdot 3^{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{1}{64} \cdot 3^{4}

3^{4} = 81

= \frac{1}{64} \cdot 81

\frac{1}{64} \cdot 81 = \frac{81}{64}

= \frac{81}{64}

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