Simplify 2x^(1/2)*3x^(1/3)

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

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

Move $x^{\frac{1}{3}}$ .

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

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

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

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $3$ by $2$ .

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

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

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

Multiply $2$ by $3$ .

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

Combine the numerators over the common denominator.

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

Add $2$ and $3$ .

$2 \cdot 3 x^{\frac{5}{6}}$

Step 3

Multiply $2$ by $3$ .

$6 x^{\frac{5}{6}}$