Algebra Examples

$\frac{{(10 a b)}^{2} (2 a^{4} b^{3})}{4 a^{5} b}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

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

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Step 1.1.1

Factor $2$ out of ${(10 a b)}^{2} (2 a^{4} b^{3})$ .

$\frac{2 ({(10 a b)}^{2} (a^{4} b^{3}))}{4 a^{5} b}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

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

$\frac{2 ({(10 a b)}^{2} (a^{4} b^{3}))}{2 (2 a^{5} b)}$

Step 1.1.2.2

Cancel the common factor.

$\frac{2 ({(10 a b)}^{2} (a^{4} b^{3}))}{2 (2 a^{5} b)}$

Step 1.1.2.3

Rewrite the expression.

$\frac{{(10 a b)}^{2} (a^{4} b^{3})}{2 a^{5} b}$

Step 1.2

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

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Step 1.2.1

Factor $a^{4}$ out of ${(10 a b)}^{2} (a^{4} b^{3})$ .

$\frac{a^{4} ({(10 a b)}^{2} (b^{3}))}{2 a^{5} b}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

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

$\frac{a^{4} ({(10 a b)}^{2} (b^{3}))}{a^{4} (2 a b)}$

Step 1.2.2.2

Cancel the common factor.

$\frac{a^{4} ({(10 a b)}^{2} (b^{3}))}{a^{4} (2 a b)}$

Step 1.2.2.3

Rewrite the expression.

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

Step 1.3

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

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Step 1.3.1

Factor $b$ out of ${(10 a b)}^{2} (b^{3})$ .

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

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $b$ out of $2 a b$ .

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

Step 1.3.2.2

Cancel the common factor.

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

Step 1.3.2.3

Rewrite the expression.

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

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $10 a b$ .

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

Step 2.2

Multiply $b^{2}$ by $b^{2}$ by adding the exponents.

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Step 2.2.1

Move $b^{2}$ .

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

Step 2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.2.3

Add $2$ and $2$ .

$\frac{{(10 a)}^{2} b^{4}}{2 a}$

Step 2.3

Apply the product rule to $10 a$ .

$\frac{10^{2} a^{2} b^{4}}{2 a}$

Step 2.4

Raise $10$ to the power of $2$ .

$\frac{100 a^{2} b^{4}}{2 a}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $100$ and $2$ .

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Step 3.1.1

Factor $2$ out of $100 a^{2} b^{4}$ .

$\frac{2 (50 a^{2} b^{4})}{2 a}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $2$ out of $2 a$ .

$\frac{2 (50 a^{2} b^{4})}{2 (a)}$

Step 3.1.2.2

Cancel the common factor.

$\frac{2 (50 a^{2} b^{4})}{2 a}$

Step 3.1.2.3

Rewrite the expression.

$\frac{50 a^{2} b^{4}}{a}$

Step 3.2

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

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Step 3.2.1

Factor $a$ out of $50 a^{2} b^{4}$ .

$\frac{a (50 a b^{4})}{a}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Raise $a$ to the power of $1$ .

$\frac{a (50 a b^{4})}{a^{1}}$

Step 3.2.2.2

Factor $a$ out of $a^{1}$ .

$\frac{a (50 a b^{4})}{a \cdot 1}$

Step 3.2.2.3

Cancel the common factor.

$\frac{a (50 a b^{4})}{a \cdot 1}$

Step 3.2.2.4

Rewrite the expression.

$\frac{50 a b^{4}}{1}$

Step 3.2.2.5

Divide $50 a b^{4}$ by $1$ .

$50 a b^{4}$