What is 9(3^{-2})^30.3^{-3} ?

The solution to 9(3^{-2})^30.3^{-3} is 0.45724…

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simplify 9(3^{-2})^30.3^{-3}

simplify

9 (3^{- 2})^{3} 0. 3^{- 3}

0.45724 \dots

Solution steps

9 (3^{- 2})^{3} \cdot 0. 3^{- 3}

(3^{- 2})^{3} : 3^{- 6}

= 9 \cdot 3^{- 6} \cdot 0. 3^{- 3}

Apply exponent rule:

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

= 3^{- 6} \cdot 9 \cdot \frac{1}{0. 3 ^{3}}

Apply exponent rule:

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

3^{- 6} = \frac{1}{3 ^{6}}

= 9 \cdot \frac{1}{3 ^{6}} \cdot \frac{1}{0. 3 ^{3}}

Multiply fractions:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{1 \cdot 1 \cdot 9}{3 ^{6} \cdot 0. 3 ^{3}}

Multiply the numbers:

1 \cdot 1 \cdot 9 = 9

= \frac{9}{3 ^{6} \cdot 0. 3 ^{3}}

Factor

9 : 3^{2}

= \frac{3 ^{2}}{3 ^{6} \cdot 0. 3 ^{3}}

Cancel

\frac{3 ^{2}}{3 ^{6} \cdot 0. 3 ^{3}} : \frac{1}{3 ^{4} \cdot 0. 3 ^{3}}

= \frac{1}{3 ^{4} \cdot 0. 3 ^{3}}

3^{4} \cdot 0. 3^{3} = 2.187

= \frac{1}{2.187}

Divide the numbers:

\frac{1}{2.187} = 0.45724 \dots

= 0.45724 \dots

34 \cdot (23 \cdot 1 0^{- 6}) \cdot 12.1

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