Algebra Examples

$\frac{4}{3} π {(\frac{3}{2})}^{3}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $\frac{3}{2}$ .

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

Step 1.2

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

$\frac{4}{3} \cdot (π \frac{27}{2^{3}})$

Step 1.3

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

$\frac{4}{3} \cdot (π \frac{27}{8})$

$\frac{4}{3} \cdot (π \frac{27}{8})$

Step 2

Combine $π$ and $\frac{27}{8}$ .

$\frac{4}{3} \cdot \frac{π \cdot 27}{8}$

Step 3

Cancel the common factor of $4$ .

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Step 3.1

Factor $4$ out of $8$ .

$\frac{4}{3} \cdot \frac{π \cdot 27}{4 (2)}$

Step 3.2

Cancel the common factor.

$\frac{4}{3} \cdot \frac{π \cdot 27}{4 \cdot 2}$

Step 3.3

Rewrite the expression.

$\frac{1}{3} \cdot \frac{π \cdot 27}{2}$

$\frac{1}{3} \cdot \frac{π \cdot 27}{2}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Factor $3$ out of $π \cdot 27$ .

$\frac{1}{3} \cdot \frac{3 (π \cdot 9)}{2}$

Step 4.2

Cancel the common factor.

$\frac{1}{3} \cdot \frac{3 (π \cdot 9)}{2}$

Step 4.3

Rewrite the expression.

$\frac{π \cdot 9}{2}$

$\frac{π \cdot 9}{2}$

Step 5

Move $9$ to the left of $π$ .

$\frac{9 π}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{9 π}{2}$

Decimal Form:

$14.13716694 \dots$

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