Simplify (x^(5/8))(x^(1/2))

$(x^{\frac{5}{8}}) (x^{\frac{1}{2}})$

Step 1

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

$x^{\frac{5}{8} + \frac{1}{2}}$

Step 2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x^{\frac{5}{8} + \frac{1}{2} \cdot \frac{4}{4}}$

Step 3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{4}{4}$ .

$x^{\frac{5}{8} + \frac{4}{2 \cdot 4}}$

Multiply $2$ by $4$ .

$x^{\frac{5}{8} + \frac{4}{8}}$

Step 4

Combine the numerators over the common denominator.

$x^{\frac{5 + 4}{8}}$

Step 5

Add $5$ and $4$ .

$x^{\frac{9}{8}}$