Calculus Examples

$\frac{4}{3} \cdot {(4)}^{\frac{3}{2}} - \frac{1}{2} \cdot {(4)}^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $4$ as $2^{2}$ .

$\frac{4}{3} \cdot {(2^{2})}^{\frac{3}{2}} - \frac{1}{2} \cdot {(4)}^{2}$

Step 1.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{4}{3} \cdot 2^{2 (\frac{3}{2})} - \frac{1}{2} \cdot {(4)}^{2}$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Cancel the common factor.

$\frac{4}{3} \cdot 2^{2 (\frac{3}{2})} - \frac{1}{2} \cdot {(4)}^{2}$

Step 1.3.2

Rewrite the expression.

$\frac{4}{3} \cdot 2^{3} - \frac{1}{2} \cdot {(4)}^{2}$

Step 1.4

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

$\frac{4}{3} \cdot 8 - \frac{1}{2} \cdot {(4)}^{2}$

Step 1.5

Multiply $\frac{4}{3} \cdot 8$ .

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Step 1.5.1

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

$\frac{4 \cdot 8}{3} - \frac{1}{2} \cdot {(4)}^{2}$

Step 1.5.2

Multiply $4$ by $8$ .

$\frac{32}{3} - \frac{1}{2} \cdot {(4)}^{2}$

Step 1.6

Raise $4$ to the power of $2$ .

$\frac{32}{3} - \frac{1}{2} \cdot 16$

Step 1.7

Cancel the common factor of $2$ .

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Step 1.7.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{32}{3} + \frac{- 1}{2} \cdot 16$

Step 1.7.2

Factor $2$ out of $16$ .

$\frac{32}{3} + \frac{- 1}{2} \cdot (2 (8))$

Step 1.7.3

Cancel the common factor.

$\frac{32}{3} + \frac{- 1}{2} \cdot (2 \cdot 8)$

Step 1.7.4

Rewrite the expression.

$\frac{32}{3} - 1 \cdot 8$

Step 1.8

Multiply $- 1$ by $8$ .

$\frac{32}{3} - 8$

Step 2

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{32}{3} - 8 \cdot \frac{3}{3}$

Step 3

Combine $- 8$ and $\frac{3}{3}$ .

$\frac{32}{3} + \frac{- 8 \cdot 3}{3}$

Step 4

Combine the numerators over the common denominator.

$\frac{32 - 8 \cdot 3}{3}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 8$ by $3$ .

$\frac{32 - 24}{3}$

Step 5.2

Subtract $24$ from $32$ .

$\frac{8}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{3}$

Decimal Form:

$2.\overline{6}$

Mixed Number Form:

$2 \frac{2}{3}$