Algebra Examples

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

Step 1

Replace the variable $r$ with $\frac{3}{2}$ in the expression.

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

Step 2

Simplify the result.

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Step 2.1

Simplify the expression.

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

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

$v (\frac{3}{2}) = \frac{4}{3} \cdot (π (\frac{27}{8}))$

Step 2.2

Combine $π$ and $\frac{27}{8}$ .

$v (\frac{3}{2}) = \frac{4}{3} \cdot \frac{π \cdot 27}{8}$

Step 2.3

Cancel the common factor of $4$ .

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Step 2.3.1

Factor $4$ out of $8$ .

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

Step 2.3.2

Cancel the common factor.

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

Step 2.3.3

Rewrite the expression.

$v (\frac{3}{2}) = \frac{1}{3} \cdot \frac{π \cdot 27}{2}$

Step 2.4

Cancel the common factor of $3$ .

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Step 2.4.1

Factor $3$ out of $π \cdot 27$ .

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

Step 2.4.2

Cancel the common factor.

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

Step 2.4.3

Rewrite the expression.

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

Step 2.5

Move $9$ to the left of $π$ .

$v (\frac{3}{2}) = \frac{9 π}{2}$

Step 2.6

The final answer is $\frac{9 π}{2}$ .

$\frac{9 π}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{9 π}{2}$

Decimal Form:

$14.13716694 \dots$

Step 4