What is 4/3 pi*3(3)^2*(-2) ?

The solution to 4/3 pi*3(3)^2*(-2) is -72pi

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simplify 4/3 pi3(3)^2(-2)

simplify

\frac{4}{3} π \cdot 3 (3)^{2} \cdot (- 2)

- 72 π

Decimal Notation

- 226.19467 \dots

Solution steps

\frac{4}{3} π 3 (3)^{2} (- 2)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

3 \cdot 3^{2} = 3^{1 + 2}

= \frac{4}{3} π 3^{1 + 2} (- 2)

Add the numbers:

1 + 2 = 3

= \frac{4}{3} π 3^{3} (- 2)

Remove parentheses:

(- a) = - a

= - \frac{4}{3} π 3^{3} \cdot 2

Multiply fractions:

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

= - \frac{4 π 3 ^{3} \cdot 2}{3}

Multiply the numbers:

4 \cdot 2 = 8

= - \frac{3 ^{3} \cdot 8 π}{3}

Cancel the common factor:

3

= - 3^{2} \cdot 8 π

3^{2} = 9

= - 9 \cdot 8 π

Multiply the numbers:

9 \cdot 8 = 72

= - 72 π

- 8 x^{2} y^{4} (3 x^{3} y^{10})

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