Simplify p^(1/4)*p^(9/4)

$p^{\frac{1}{4}} \cdot p^{\frac{9}{4}}$

Step 1

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

$p^{\frac{1}{4} + \frac{9}{4}}$

Step 2

Combine the numerators over the common denominator.

$p^{\frac{1 + 9}{4}}$

Step 3

Add $1$ and $9$ .

$p^{\frac{10}{4}}$

Step 4

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10$ .

$p^{\frac{2 (5)}{4}}$

Cancel the common factors.

Factor $2$ out of $4$ .

$p^{\frac{2 \cdot 5}{2 \cdot 2}}$

Cancel the common factor.

$p^{\frac{2 \cdot 5}{2 \cdot 2}}$

Rewrite the expression.

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