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

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

Step 1

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

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

Step 2

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

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

Step 3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $2$ by $2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Add $2$ and $3$ .

$x^{\frac{5}{4}}$