Evaluate 5^(1/2)*5^(3/2)

$5^{\frac{1}{2}} \cdot 5^{\frac{3}{2}}$

Step 1

Multiply $5^{\frac{1}{2}}$ by $5^{\frac{3}{2}}$ by adding the exponents.

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

$5^{\frac{1}{2} + \frac{3}{2}}$

Combine the numerators over the common denominator.

$5^{\frac{1 + 3}{2}}$

Add $1$ and $3$ .

$5^{\frac{4}{2}}$

Divide $4$ by $2$ .

$5^{2}$

Step 2

Raise $5$ to the power of $2$ .

$25$