Simplify 4/3*3.14*(850mi)^3

$\frac{4}{3} \cdot 3.14 \cdot {(850 m i)}^{3}$

Multiply $\frac{4}{3} \cdot 3.14$ .

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Combine $\frac{4}{3}$ and $3.14$ .

$\frac{4 \cdot 3.14}{3} \cdot {(850 m i)}^{3}$

Multiply $4$ by $3.14$ .

$\frac{12.56}{3} \cdot {(850 m i)}^{3}$

Divide $12.56$ by $3$ .

$4.18\overline{6} \cdot {(850 m i)}^{3}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Apply the product rule to $850 m i$ .

$4.18\overline{6} \cdot ({(850 m)}^{3} i^{3})$

Apply the product rule to $850 m$ .

$4.18\overline{6} \cdot (850^{3} m^{3} i^{3})$

Raise $850$ to the power of $3$ .

$4.18\overline{6} \cdot (614125000 m^{3} i^{3})$

Factor out $i^{2}$ .

$4.18\overline{6} \cdot (614125000 m^{3} (i^{2} \cdot i))$

Rewrite $i^{2}$ as $- 1$ .

$4.18\overline{6} \cdot (614125000 m^{3} (- 1 \cdot i))$

Rewrite $- 1 i$ as $- i$ .

$4.18\overline{6} \cdot (614125000 m^{3} (- i))$

Multiply $- 1$ by $614125000$ .

$4.18\overline{6} \cdot (- 614125000 m^{3} i)$

Multiply $- 614125000$ by $4.18\overline{6}$ .

$- 2571136666.\overline{6} m^{3} i$

Simplify 4/3*3.14*(850mi)^3

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