Simplify x^(2/3)*x^(1/4)

$x^{\frac{2}{3}} \cdot x^{\frac{1}{4}}$

Step 1

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

$x^{\frac{2}{3} + \frac{1}{4}}$

Step 2

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x^{\frac{2}{3} \cdot \frac{4}{4} + \frac{1}{4}}$

Step 3

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x^{\frac{2}{3} \cdot \frac{4}{4} + \frac{1}{4} \cdot \frac{3}{3}}$

Step 4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$x^{\frac{2 \cdot 4}{3 \cdot 4} + \frac{1}{4} \cdot \frac{3}{3}}$

Multiply $3$ by $4$ .

$x^{\frac{2 \cdot 4}{12} + \frac{1}{4} \cdot \frac{3}{3}}$

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$x^{\frac{2 \cdot 4}{12} + \frac{3}{4 \cdot 3}}$

Multiply $4$ by $3$ .

$x^{\frac{2 \cdot 4}{12} + \frac{3}{12}}$

Step 5

Combine the numerators over the common denominator.

$x^{\frac{2 \cdot 4 + 3}{12}}$

Step 6

Simplify the numerator.

Multiply $2$ by $4$ .

$x^{\frac{8 + 3}{12}}$

Add $8$ and $3$ .

$x^{\frac{11}{12}}$