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Popular >

simplify 3^{-5/3}*0.09

Solution

simplify

3^{- \frac{5}{3}} \cdot 0.09

Solution

\frac{3 ^{\frac{1}{3}}}{100}

+1

Decimal Notation

0.01442 \dots

Solution steps

3^{- \frac{5}{3}} \cdot 0.09

Apply exponent rule:

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

3^{- \frac{5}{3}} = \frac{1}{3 ^{\frac{5}{3}}}

= \frac{1}{3 ^{\frac{5}{3}}} \cdot 0.09

3^{\frac{5}{3}} = 3 \cdot 3^{\frac{2}{3}}

= \frac{1}{3 \cdot 3 ^{\frac{2}{3}}} \cdot 0.09

\frac{1}{3 \cdot 3 ^{\frac{2}{3}}} \cdot 0.09 = \frac{0.09}{3 ^{\frac{2}{3}} \cdot 3}

= \frac{0.09}{3 ^{\frac{2}{3}} \cdot 3}

\frac{0.09}{3 ^{\frac{2}{3}} \cdot 3} = \frac{9}{300 \cdot 3 ^{\frac{2}{3}}}

= \frac{9}{300 \cdot 3 ^{\frac{2}{3}}}

Factor the number:

9 = 3 \cdot 3

= \frac{3 \cdot 3}{300 \cdot 3 ^{\frac{2}{3}}}

Factor the number:

300 = 3 \cdot 100

= \frac{3 \cdot 3}{3 \cdot 100 \cdot 3 ^{\frac{2}{3}}}

Cancel the common factor:

3

= \frac{3}{100 \cdot 3 ^{\frac{2}{3}}}

Simplify

\frac{3}{3 ^{\frac{2}{3}}} : 3^{\frac{1}{3}}

= \frac{3 ^{\frac{1}{3}}}{100}

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Frequently Asked Questions (FAQ)

What is 3^{-5/3}*0.09 ?
The solution to 3^{-5/3}*0.09 is (3^{1/3})/(100)