Calculus Examples

$3^{\frac{1}{2}} \cdot \frac{2}{3} \cdot 12^{\frac{3}{2}}$

Step 1

Combine $3^{\frac{1}{2}}$ and $\frac{2}{3}$ .

$\frac{3^{\frac{1}{2}} \cdot 2}{3} \cdot 12^{\frac{3}{2}}$

Step 2

Simplify the expression.

Tap for more steps...

Step 2.1

Move $2$ to the left of $3^{\frac{1}{2}}$ .

$\frac{2 \cdot 3^{\frac{1}{2}}}{3} \cdot 12^{\frac{3}{2}}$

Step 2.2

Move $3^{\frac{1}{2}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{2}{3 \cdot 3^{- \frac{1}{2}}} \cdot 12^{\frac{3}{2}}$

Step 3

Multiply $3$ by $3^{- \frac{1}{2}}$ by adding the exponents.

Tap for more steps...

Step 3.1

Multiply $3$ by $3^{- \frac{1}{2}}$ .

Tap for more steps...

Step 3.1.1

Raise $3$ to the power of $1$ .

$\frac{2}{3^{1} \cdot 3^{- \frac{1}{2}}} \cdot 12^{\frac{3}{2}}$

Step 3.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2}{3^{1 - \frac{1}{2}}} \cdot 12^{\frac{3}{2}}$

Step 3.2

Write $1$ as a fraction with a common denominator.

$\frac{2}{3^{\frac{2}{2} - \frac{1}{2}}} \cdot 12^{\frac{3}{2}}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{2}{3^{\frac{2 - 1}{2}}} \cdot 12^{\frac{3}{2}}$

Step 3.4

Subtract $1$ from $2$ .

$\frac{2}{3^{\frac{1}{2}}} \cdot 12^{\frac{3}{2}}$

Step 4

Combine $\frac{2}{3^{\frac{1}{2}}}$ and $12^{\frac{3}{2}}$ .

$\frac{2 \cdot 12^{\frac{3}{2}}}{3^{\frac{1}{2}}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \cdot 12^{\frac{3}{2}}}{3^{\frac{1}{2}}}$

Decimal Form:

$48$