Algebra Examples

${(a^{\frac{1}{2}} \cdot b^{\frac{1}{3}})}^{\frac{1}{2}}$

Step 1

Apply the product rule to $a^{\frac{1}{2}} b^{\frac{1}{3}}$ .

${(a^{\frac{1}{2}})}^{\frac{1}{2}} {(b^{\frac{1}{3}})}^{\frac{1}{2}}$

Step 2

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

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Step 2.1

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

$a^{\frac{1}{2} \cdot \frac{1}{2}} {(b^{\frac{1}{3}})}^{\frac{1}{2}}$

Step 2.2

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

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Step 2.2.1

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

$a^{\frac{1}{2 \cdot 2}} {(b^{\frac{1}{3}})}^{\frac{1}{2}}$

Step 2.2.2

Multiply $2$ by $2$ .

$a^{\frac{1}{4}} {(b^{\frac{1}{3}})}^{\frac{1}{2}}$

Step 3

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

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Step 3.1

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

$a^{\frac{1}{4}} b^{\frac{1}{3} \cdot \frac{1}{2}}$

Step 3.2

Multiply $\frac{1}{3} \cdot \frac{1}{2}$ .

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Step 3.2.1

Multiply $\frac{1}{3}$ by $\frac{1}{2}$ .

$a^{\frac{1}{4}} b^{\frac{1}{3 \cdot 2}}$

Step 3.2.2

Multiply $3$ by $2$ .

$a^{\frac{1}{4}} b^{\frac{1}{6}}$