Algebra Examples

$\frac{24 a^{5} b^{2}}{{(2 a b)}^{4}}$

Step 1

Simplify the denominator.

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Step 1.1

Apply the product rule to $2 a b$ .

$\frac{24 a^{5} b^{2}}{{(2 a)}^{4} b^{4}}$

Step 1.2

Apply the product rule to $2 a$ .

$\frac{24 a^{5} b^{2}}{2^{4} a^{4} b^{4}}$

Step 1.3

Raise $2$ to the power of $4$ .

$\frac{24 a^{5} b^{2}}{16 a^{4} b^{4}}$

$\frac{24 a^{5} b^{2}}{16 a^{4} b^{4}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $24$ and $16$ .

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Step 2.1.1

Factor $8$ out of $24 a^{5} b^{2}$ .

$\frac{8 (3 a^{5} b^{2})}{16 a^{4} b^{4}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $8$ out of $16 a^{4} b^{4}$ .

$\frac{8 (3 a^{5} b^{2})}{8 (2 a^{4} b^{4})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{8 (3 a^{5} b^{2})}{8 (2 a^{4} b^{4})}$

Step 2.1.2.3

Rewrite the expression.

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

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

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

Step 2.2

Cancel the common factor of $a^{5}$ and $a^{4}$ .

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Step 2.2.1

Factor $a^{4}$ out of $3 a^{5} b^{2}$ .

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

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

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

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

Step 2.2.2.2

Cancel the common factor.

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

Step 2.2.2.3

Rewrite the expression.

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

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

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

Step 2.3

Cancel the common factor of $b^{2}$ and $b^{4}$ .

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Step 2.3.1

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

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

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

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

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

Step 2.3.2.2

Cancel the common factor.

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

Step 2.3.2.3

Rewrite the expression.

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

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

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

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$