Trigonometry Examples

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

Step 1

Rewrite using the commutative property of multiplication.

$4 \cdot - 3 x^{2} x^{\frac{4}{3}}$

Step 2

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

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Step 2.1

Move $x^{\frac{4}{3}}$ .

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

Step 2.2

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

$4 \cdot - 3 x^{\frac{4}{3} + 2}$

Step 2.3

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

$4 \cdot - 3 x^{\frac{4}{3} + 2 \cdot \frac{3}{3}}$

Step 2.4

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

$4 \cdot - 3 x^{\frac{4}{3} + \frac{2 \cdot 3}{3}}$

Step 2.5

Combine the numerators over the common denominator.

$4 \cdot - 3 x^{\frac{4 + 2 \cdot 3}{3}}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $2$ by $3$ .

$4 \cdot - 3 x^{\frac{4 + 6}{3}}$

Step 2.6.2

Add $4$ and $6$ .

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

Step 3

Multiply $4$ by $- 3$ .

$- 12 x^{\frac{10}{3}}$