Simplify x1/3(x1/2+2x^2)

$x \frac{1}{3} (x \frac{1}{2} + 2 x^{2})$

Step 1

Combine $x$ and $\frac{1}{3}$ .

$\frac{x}{3} \cdot (x (\frac{1}{2}) + 2 x^{2})$

Step 2

Combine $x$ and $\frac{1}{2}$ .

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

Step 3

Apply the distributive property.

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

Step 4

Multiply $\frac{x}{3} \cdot \frac{x}{2}$ .

Multiply $\frac{x}{3}$ by $\frac{x}{2}$ .

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

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

$\frac{x^{1} x}{3 \cdot 2} + \frac{x}{3} (2 x^{2})$

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

$\frac{x^{1} x^{1}}{3 \cdot 2} + \frac{x}{3} (2 x^{2})$

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

$\frac{x^{1 + 1}}{3 \cdot 2} + \frac{x}{3} (2 x^{2})$

Add $1$ and $1$ .

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

Multiply $3$ by $2$ .

$\frac{x^{2}}{6} + \frac{x}{3} (2 x^{2})$

Step 5

Rewrite using the commutative property of multiplication.

$\frac{x^{2}}{6} + 2 \frac{x}{3} x^{2}$

Step 6

Simplify each term.

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

$\frac{x^{2}}{6} + \frac{2 x}{3} x^{2}$

Multiply $\frac{2 x}{3} x^{2}$ .

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

$\frac{x^{2}}{6} + \frac{2 x \cdot x^{2}}{3}$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$\frac{x^{2}}{6} + \frac{2 (x^{2} x)}{3}$

Multiply $x^{2}$ by $x$ .

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

$\frac{x^{2}}{6} + \frac{2 (x^{2} x^{1})}{3}$

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

$\frac{x^{2}}{6} + \frac{2 x^{2 + 1}}{3}$

Add $2$ and $1$ .

$\frac{x^{2}}{6} + \frac{2 x^{3}}{3}$