Precalculus Examples

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

Step 1

Multiply $x^{\frac{4}{3}}$ by $x^{2}$ by adding the exponents.

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Step 1.1

Move $x^{2}$ .

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

Step 1.2

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

$4 x^{2 + \frac{4}{3}} \cdot (3 y^{\frac{4}{3}})$

Step 1.3

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$4 x^{2 \cdot \frac{3}{3} + \frac{4}{3}} \cdot (3 y^{\frac{4}{3}})$

Step 1.4

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

$4 x^{\frac{2 \cdot 3}{3} + \frac{4}{3}} \cdot (3 y^{\frac{4}{3}})$

Step 1.5

Combine the numerators over the common denominator.

$4 x^{\frac{2 \cdot 3 + 4}{3}} \cdot (3 y^{\frac{4}{3}})$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $2$ by $3$ .

$4 x^{\frac{6 + 4}{3}} \cdot (3 y^{\frac{4}{3}})$

Step 1.6.2

Add $6$ and $4$ .

$4 x^{\frac{10}{3}} \cdot (3 y^{\frac{4}{3}})$

Step 2

Rewrite using the commutative property of multiplication.

$4 \cdot 3 x^{\frac{10}{3}} y^{\frac{4}{3}}$

Step 3

Multiply $4$ by $3$ .

$12 x^{\frac{10}{3}} y^{\frac{4}{3}}$