Calculus Examples

$\frac{{(184)}^{\frac{3}{2}}}{21} - \frac{{(16)}^{\frac{3}{2}}}{21}$

Step 1

Combine the numerators over the common denominator.

$\frac{{(184)}^{\frac{3}{2}} - {(16)}^{\frac{3}{2}}}{21}$

Step 2

Simplify each term.

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Step 2.1

Rewrite $16$ as $4^{2}$ .

$\frac{{(184)}^{\frac{3}{2}} - {(4^{2})}^{\frac{3}{2}}}{21}$

Step 2.2

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

$\frac{{(184)}^{\frac{3}{2}} - 4^{2 (\frac{3}{2})}}{21}$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Cancel the common factor.

$\frac{{(184)}^{\frac{3}{2}} - 4^{2 (\frac{3}{2})}}{21}$

Step 2.3.2

Rewrite the expression.

$\frac{{(184)}^{\frac{3}{2}} - 4^{3}}{21}$

Step 2.4

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

$\frac{{(184)}^{\frac{3}{2}} - 1 \cdot 64}{21}$

Step 2.5

Multiply $- 1$ by $64$ .

$\frac{{(184)}^{\frac{3}{2}} - 64}{21}$

$\frac{184^{\frac{3}{2}} - 64}{21}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{184^{\frac{3}{2}} - 64}{21}$

Decimal Form:

$115.80463970 \dots$