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Popular >

simplify 4/3 pi(5/2)^3

Solution

simplify

\frac{4}{3} π (\frac{5}{2})^{3}

Solution

\frac{125 π}{6}

+1

Decimal Notation

65.44984 \dots

Solution steps

\frac{4}{3} π (\frac{5}{2})^{3}

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

= π \frac{4}{3} \cdot \frac{5 ^{3}}{2 ^{3}}

Multiply fractions:

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

= \frac{4 \cdot 5 ^{3} π}{3 \cdot 2 ^{3}}

Factor

4 : 2^{2}

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

Cancel

\frac{2 ^{2} \cdot 5 ^{3} π}{3 \cdot 2 ^{3}} : \frac{5 ^{3} π}{3 \cdot 2}

= \frac{5 ^{3} π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{5 ^{3} π}{6}

5^{3} = 125

= \frac{125 π}{6}

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Frequently Asked Questions (FAQ)

What is 4/3 pi(5/2)^3 ?
The solution to 4/3 pi(5/2)^3 is (125pi)/6