Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $2$ by $2$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

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 $- 1$ .

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