Algebra Examples

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

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Raise $2$ to the power of $3$ .

$8 {(a^{\frac{1}{2}})}^{3} {(b^{\frac{1}{3}})}^{3}$

Step 3

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

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Step 3.1

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

$8 a^{\frac{1}{2} \cdot 3} {(b^{\frac{1}{3}})}^{3}$

Step 3.2

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

$8 a^{\frac{3}{2}} {(b^{\frac{1}{3}})}^{3}$

Step 4

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

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Step 4.1

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

$8 a^{\frac{3}{2}} b^{\frac{1}{3} \cdot 3}$

Step 4.2

Cancel the common factor of $3$ .

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Step 4.2.1

Cancel the common factor.

$8 a^{\frac{3}{2}} b^{\frac{1}{3} \cdot 3}$

Step 4.2.2

Rewrite the expression.

$8 a^{\frac{3}{2}} b^{1}$

Step 5

Simplify.

$8 a^{\frac{3}{2}} b$

Step 6

Reorder factors in $8 a^{\frac{3}{2}} b$ .

$8 b a^{\frac{3}{2}}$