Pre-Algebra Examples

 $\begin{array}{r} r = & \frac{4}{3} \end{array}$

Step 1

The volume of a sphere is equal to $\frac{4}{3}$ times Pi $π$ times the radius cubed.

$\frac{4}{3} \cdot π \cdot {(r a d i u s)}^{3}$

Step 2

Substitute the value of the radius $r = \frac{4}{3}$ into the formula to find the volume of the sphere. Pi $π$ is approximately equal to $3.14$ .

$\frac{4}{3} \cdot π \cdot {(\frac{4}{3})}^{3}$

Step 3

Multiply $\frac{4}{3}$ by ${(\frac{4}{3})}^{3}$ by adding the exponents.

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Step 3.1

Move ${(\frac{4}{3})}^{3}$ .

${(\frac{4}{3})}^{3} \frac{4}{3} \cdot π$

Step 3.2

Multiply ${(\frac{4}{3})}^{3}$ by $\frac{4}{3}$ .

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Step 3.2.1

Raise $\frac{4}{3}$ to the power of $1$ .

${(\frac{4}{3})}^{3} {(\frac{4}{3})}^{1} \cdot π$

Step 3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{4}{3})}^{3 + 1} \cdot π$

Step 3.3

Add $3$ and $1$ .

${(\frac{4}{3})}^{4} \cdot π$

Step 4

Simplify the expression.

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Step 4.1

Apply the product rule to $\frac{4}{3}$ .

$\frac{4^{4}}{3^{4}} \cdot π$

Step 4.2

Raise $4$ to the power of $4$ .

$\frac{256}{3^{4}} \cdot π$

Step 4.3

Raise $3$ to the power of $4$ .

$\frac{256}{81} \cdot π$

Step 5

Combine $\frac{256}{81}$ and $π$ .

$\frac{256 π}{81}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{256 π}{81}$

Decimal Form:

$9.92898418 \dots$