Simplify the Radical Expression (x^(7/8))(x^(1/4))

$(x^{\frac{7}{8}}) (x^{\frac{1}{4}})$

Step 1

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

$x^{\frac{7}{8} + \frac{1}{4}}$

Step 2

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

$x^{\frac{7}{8} + \frac{1}{4} \cdot \frac{2}{2}}$

Step 3

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

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

$x^{\frac{7}{8} + \frac{2}{4 \cdot 2}}$

Multiply $4$ by $2$ .

$x^{\frac{7}{8} + \frac{2}{8}}$

Step 4

Combine the numerators over the common denominator.

$x^{\frac{7 + 2}{8}}$

Step 5

Add $7$ and $2$ .

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