Simplify 7^(1/4)*7^(1/2)

$7^{\frac{1}{4}} \cdot 7^{\frac{1}{2}}$

Step 1

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

$7^{\frac{1}{4} + \frac{1}{2}}$

Step 2

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

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

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 $\frac{2}{2}$ .

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

Multiply $2$ by $2$ .

$7^{\frac{1}{4} + \frac{2}{4}}$

Step 4

Combine the numerators over the common denominator.

$7^{\frac{1 + 2}{4}}$

Step 5

Add $1$ and $2$ .

$7^{\frac{3}{4}}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$7^{\frac{3}{4}}$

Decimal Form:

$4.30351707 \dots$