Pre-Algebra Examples

${(\frac{2 a^{5} b^{6}}{4 b^{3}})}^{2}$

Step 1

Cancel the common factor of $2$ and $4$ .

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Step 1.1

Factor $2$ out of $2 a^{5} b^{6}$ .

${(\frac{2 (a^{5} b^{6})}{4 b^{3}})}^{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $4 b^{3}$ .

${(\frac{2 (a^{5} b^{6})}{2 (2 b^{3})})}^{2}$

Step 1.2.2

Cancel the common factor.

${(\frac{2 (a^{5} b^{6})}{2 (2 b^{3})})}^{2}$

Step 1.2.3

Rewrite the expression.

${(\frac{a^{5} b^{6}}{2 b^{3}})}^{2}$

Step 2

Cancel the common factor of $b^{6}$ and $b^{3}$ .

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Step 2.1

Factor $b^{3}$ out of $a^{5} b^{6}$ .

${(\frac{b^{3} (a^{5} b^{3})}{2 b^{3}})}^{2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $b^{3}$ out of $2 b^{3}$ .

${(\frac{b^{3} (a^{5} b^{3})}{b^{3} \cdot 2})}^{2}$

Step 2.2.2

Cancel the common factor.

${(\frac{b^{3} (a^{5} b^{3})}{b^{3} \cdot 2})}^{2}$

Step 2.2.3

Rewrite the expression.

${(\frac{a^{5} b^{3}}{2})}^{2}$

Step 3

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

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Step 3.1

Apply the product rule to $\frac{a^{5} b^{3}}{2}$ .

$\frac{{(a^{5} b^{3})}^{2}}{2^{2}}$

Step 3.2

Apply the product rule to $a^{5} b^{3}$ .

$\frac{{(a^{5})}^{2} {(b^{3})}^{2}}{2^{2}}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply the exponents in ${(a^{5})}^{2}$ .

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Step 4.1.1

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

$\frac{a^{5 \cdot 2} {(b^{3})}^{2}}{2^{2}}$

Step 4.1.2

Multiply $5$ by $2$ .

$\frac{a^{10} {(b^{3})}^{2}}{2^{2}}$

Step 4.2

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

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Step 4.2.1

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

$\frac{a^{10} b^{3 \cdot 2}}{2^{2}}$

Step 4.2.2

Multiply $3$ by $2$ .

$\frac{a^{10} b^{6}}{2^{2}}$

Step 5

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

$\frac{a^{10} b^{6}}{4}$