Algebra Examples

$π {(\frac{r}{2})}^{3} (\frac{4}{3 π r^{2}})$

Step 1

Simplify terms.

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Step 1.1

Cancel the common factor of $π$ .

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Step 1.1.1

Factor $π$ out of $π {(\frac{r}{2})}^{3}$ .

$π ({(\frac{r}{2})}^{3}) \frac{4}{3 π r^{2}}$

Step 1.1.2

Factor $π$ out of $3 π r^{2}$ .

$π ({(\frac{r}{2})}^{3}) \frac{4}{π (3 r^{2})}$

Step 1.1.3

Cancel the common factor.

$π {(\frac{r}{2})}^{3} \frac{4}{π (3 r^{2})}$

Step 1.1.4

Rewrite the expression.

${(\frac{r}{2})}^{3} \frac{4}{3 r^{2}}$

${(\frac{r}{2})}^{3} \frac{4}{3 r^{2}}$

Step 1.2

Combine ${(\frac{r}{2})}^{3}$ and $\frac{4}{3 r^{2}}$ .

$\frac{{(\frac{r}{2})}^{3} \cdot 4}{3 r^{2}}$

$\frac{{(\frac{r}{2})}^{3} \cdot 4}{3 r^{2}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $\frac{r}{2}$ .

$\frac{\frac{r^{3}}{2^{3}} \cdot 4}{3 r^{2}}$

Step 2.2

Raise $2$ to the power of $3$ .

$\frac{\frac{r^{3}}{8} \cdot 4}{3 r^{2}}$

$\frac{\frac{r^{3}}{8} \cdot 4}{3 r^{2}}$

Step 3

Simplify terms.

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Step 3.1

Combine $\frac{r^{3}}{8}$ and $4$ .

$\frac{\frac{r^{3} \cdot 4}{8}}{3 r^{2}}$

Step 3.2

Reduce the expression $\frac{r^{3} \cdot 4}{8}$ by cancelling the common factors.

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Step 3.2.1

Factor $4$ out of $r^{3} \cdot 4$ .

$\frac{\frac{4 \cdot r^{3}}{8}}{3 r^{2}}$

Step 3.2.2

Factor $4$ out of $8$ .

$\frac{\frac{4 \cdot r^{3}}{4 \cdot 2}}{3 r^{2}}$

Step 3.2.3

Cancel the common factor.

$\frac{\frac{4 \cdot r^{3}}{4 \cdot 2}}{3 r^{2}}$

Step 3.2.4

Rewrite the expression.

$\frac{\frac{r^{3}}{2}}{3 r^{2}}$

$\frac{\frac{r^{3}}{2}}{3 r^{2}}$

$\frac{\frac{r^{3}}{2}}{3 r^{2}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{r^{3}}{2} \cdot \frac{1}{3 r^{2}}$

Step 5

Simplify terms.

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Step 5.1

Combine.

$\frac{r^{3} \cdot 1}{2 (3 r^{2})}$

Step 5.2

Cancel the common factor of $r^{3}$ and $r^{2}$ .

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Step 5.2.1

Factor $r^{2}$ out of $r^{3} \cdot 1$ .

$\frac{r^{2} (r \cdot 1)}{2 (3 r^{2})}$

Step 5.2.2

Cancel the common factors.

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Step 5.2.2.1

Factor $r^{2}$ out of $2 (3 r^{2})$ .

$\frac{r^{2} (r \cdot 1)}{r^{2} (2 \cdot (3))}$

Step 5.2.2.2

Cancel the common factor.

$\frac{r^{2} (r \cdot 1)}{r^{2} (2 \cdot (3))}$

Step 5.2.2.3

Rewrite the expression.

$\frac{r \cdot 1}{2 \cdot (3)}$

$\frac{r \cdot 1}{2 \cdot (3)}$

$\frac{r \cdot 1}{2 \cdot (3)}$

Step 5.3

Multiply $r$ by $1$ .

$\frac{r}{2 \cdot (3)}$

$\frac{r}{2 \cdot (3)}$

Step 6

Multiply $2$ by $3$ .

$\frac{r}{6}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$