Algebra Examples

${(\frac{p^{2} q^{7}}{q^{4}})}^{\frac{1}{2}}$

Step 1

Cancel the common factor of $q^{7}$ and $q^{4}$ .

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Step 1.1

Factor $q^{4}$ out of $p^{2} q^{7}$ .

${(\frac{q^{4} (p^{2} q^{3})}{q^{4}})}^{\frac{1}{2}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Multiply by $1$ .

${(\frac{q^{4} (p^{2} q^{3})}{q^{4} \cdot 1})}^{\frac{1}{2}}$

Step 1.2.2

Cancel the common factor.

${(\frac{q^{4} (p^{2} q^{3})}{q^{4} \cdot 1})}^{\frac{1}{2}}$

Step 1.2.3

Rewrite the expression.

${(\frac{p^{2} q^{3}}{1})}^{\frac{1}{2}}$

Step 1.2.4

Divide $p^{2} q^{3}$ by $1$ .

${(p^{2} q^{3})}^{\frac{1}{2}}$

Step 2

Apply basic rules of exponents.

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Step 2.1

Apply the product rule to $p^{2} q^{3}$ .

${(p^{2})}^{\frac{1}{2}} {(q^{3})}^{\frac{1}{2}}$

Step 2.2

Multiply the exponents in ${(p^{2})}^{\frac{1}{2}}$ .

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Step 2.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$p^{2 (\frac{1}{2})} {(q^{3})}^{\frac{1}{2}}$

Step 2.2.2

Cancel the common factor of $2$ .

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Step 2.2.2.1

Cancel the common factor.

$p^{2 (\frac{1}{2})} {(q^{3})}^{\frac{1}{2}}$

Step 2.2.2.2

Rewrite the expression.

$p^{1} {(q^{3})}^{\frac{1}{2}}$

Step 3

Simplify.

$p {(q^{3})}^{\frac{1}{2}}$

Step 4

Multiply the exponents in ${(q^{3})}^{\frac{1}{2}}$ .

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Step 4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$p q^{3 (\frac{1}{2})}$

Step 4.2

Combine $3$ and $\frac{1}{2}$ .

$p q^{\frac{3}{2}}$