Simplify (p^(1/2)*p^(1/4))- fourth root of 16p^3

$(p^{\frac{1}{2}} \cdot p^{\frac{1}{4}}) - \sqrt[4]{16 p^{3}}$

Step 1

Multiply $p^{\frac{1}{2}}$ by $p^{\frac{1}{4}}$ by adding the exponents.

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

$p^{\frac{1}{2} + \frac{1}{4}} - \sqrt[4]{16 p^{3}}$

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

$p^{\frac{1}{2} \cdot \frac{2}{2} + \frac{1}{4}} - \sqrt[4]{16 p^{3}}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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

$p^{\frac{2}{2 \cdot 2} + \frac{1}{4}} - \sqrt[4]{16 p^{3}}$

Multiply $2$ by $2$ .

$p^{\frac{2}{4} + \frac{1}{4}} - \sqrt[4]{16 p^{3}}$

Combine the numerators over the common denominator.

$p^{\frac{2 + 1}{4}} - \sqrt[4]{16 p^{3}}$

Add $2$ and $1$ .

$p^{\frac{3}{4}} - \sqrt[4]{16 p^{3}}$

Step 2

Rewrite $16$ as $2^{4}$ .

$p^{\frac{3}{4}} - \sqrt[4]{2^{4} p^{3}}$

Step 3

Pull terms out from under the radical.

$p^{\frac{3}{4}} - (2 \sqrt[4]{p^{3}})$

Step 4

Multiply $2$ by $- 1$ .

$p^{\frac{3}{4}} - 2 \sqrt[4]{p^{3}}$