Basic Math Examples

$(\frac{6 a^{2} b^{3}}{{(a^{2} b^{2})}^{3}}) (\frac{{(a^{5} b^{2})}^{3}}{10 a b})$

Step 1

Simplify terms.

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Step 1.1

Combine.

$\frac{6 a^{2} b^{3} {(a^{5} b^{2})}^{3}}{{(a^{2} b^{2})}^{3} (10 a b)}$

Step 1.2

Cancel the common factor of $6$ and $10$ .

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Step 1.2.1

Factor $2$ out of $6 a^{2} b^{3} {(a^{5} b^{2})}^{3}$ .

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

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

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

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

Step 1.2.2.2

Cancel the common factor.

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

Step 1.2.2.3

Rewrite the expression.

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

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

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

Step 1.3.2.2

Cancel the common factor.

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

Step 1.3.2.3

Rewrite the expression.

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

Step 1.4

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

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Step 1.4.1

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

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

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

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

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

Step 1.4.2.2

Cancel the common factor.

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

Step 1.4.2.3

Rewrite the expression.

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

Step 2.2

Multiply the exponents in ${(a^{5})}^{3}$ .

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Step 2.2.1

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

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

Step 2.2.2

Multiply $5$ by $3$ .

$\frac{3 a b^{2} a^{15} {(b^{2})}^{3}}{{(a^{2} b^{2})}^{3} \cdot 5}$

Step 2.3

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

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Step 2.3.1

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

$\frac{3 a b^{2} a^{15} b^{2 \cdot 3}}{{(a^{2} b^{2})}^{3} \cdot 5}$

Step 2.3.2

Multiply $2$ by $3$ .

$\frac{3 a b^{2} a^{15} b^{6}}{{(a^{2} b^{2})}^{3} \cdot 5}$

Step 2.4

Combine exponents.

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Step 2.4.1

Multiply $a$ by $a^{15}$ by adding the exponents.

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Step 2.4.1.1

Move $a^{15}$ .

$\frac{3 (a^{15} a) b^{2} b^{6}}{{(a^{2} b^{2})}^{3} \cdot 5}$

Step 2.4.1.2

Multiply $a^{15}$ by $a$ .

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Step 2.4.1.2.1

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

$\frac{3 (a^{15} a^{1}) b^{2} b^{6}}{{(a^{2} b^{2})}^{3} \cdot 5}$

Step 2.4.1.2.2

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

$\frac{3 a^{15 + 1} b^{2} b^{6}}{{(a^{2} b^{2})}^{3} \cdot 5}$

Step 2.4.1.3

Add $15$ and $1$ .

$\frac{3 a^{16} b^{2} b^{6}}{{(a^{2} b^{2})}^{3} \cdot 5}$

Step 2.4.2

Multiply $b^{2}$ by $b^{6}$ by adding the exponents.

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Step 2.4.2.1

Move $b^{6}$ .

$\frac{3 a^{16} (b^{6} b^{2})}{{(a^{2} b^{2})}^{3} \cdot 5}$

Step 2.4.2.2

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

$\frac{3 a^{16} b^{6 + 2}}{{(a^{2} b^{2})}^{3} \cdot 5}$

Step 2.4.2.3

Add $6$ and $2$ .

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

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $a^{2} b^{2}$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Multiply $2$ by $3$ .

$\frac{3 a^{16} b^{8}}{a^{6} {(b^{2})}^{3} \cdot 5}$

Step 3.3

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

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Step 3.3.1

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

$\frac{3 a^{16} b^{8}}{a^{6} b^{2 \cdot 3} \cdot 5}$

Step 3.3.2

Multiply $2$ by $3$ .

$\frac{3 a^{16} b^{8}}{a^{6} b^{6} \cdot 5}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $a^{16}$ and $a^{6}$ .

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Step 4.1.1

Factor $a^{6}$ out of $3 a^{16} b^{8}$ .

$\frac{a^{6} (3 a^{10} b^{8})}{a^{6} b^{6} \cdot 5}$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

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

$\frac{a^{6} (3 a^{10} b^{8})}{a^{6} (b^{6} \cdot 5)}$

Step 4.1.2.2

Cancel the common factor.

$\frac{a^{6} (3 a^{10} b^{8})}{a^{6} (b^{6} \cdot 5)}$

Step 4.1.2.3

Rewrite the expression.

$\frac{3 a^{10} b^{8}}{b^{6} \cdot 5}$

Step 4.2

Cancel the common factor of $b^{8}$ and $b^{6}$ .

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Step 4.2.1

Factor $b^{6}$ out of $3 a^{10} b^{8}$ .

$\frac{b^{6} (3 a^{10} b^{2})}{b^{6} \cdot 5}$

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

Factor $b^{6}$ out of $b^{6} \cdot 5$ .

$\frac{b^{6} (3 a^{10} b^{2})}{b^{6} (5)}$

Step 4.2.2.2

Cancel the common factor.

$\frac{b^{6} (3 a^{10} b^{2})}{b^{6} \cdot 5}$

Step 4.2.2.3

Rewrite the expression.

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