Trigonometry Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Multiply $3$ by $5$ .

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $2$ by $5$ .

$\frac{a^{15} \cdot b^{10}}{a b}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $a^{15}$ and $a$ .

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Step 2.1.1

Factor $a$ out of $a^{15} \cdot b^{10}$ .

$\frac{a (a^{14} \cdot b^{10})}{a b}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $a$ out of $a b$ .

$\frac{a (a^{14} \cdot b^{10})}{a (b)}$

Step 2.1.2.2

Cancel the common factor.

$\frac{a (a^{14} \cdot b^{10})}{a b}$

Step 2.1.2.3

Rewrite the expression.

$\frac{a^{14} \cdot b^{10}}{b}$

Step 2.2

Cancel the common factor of $b^{10}$ and $b$ .

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Step 2.2.1

Factor $b$ out of $a^{14} \cdot b^{10}$ .

$\frac{b (a^{14} \cdot b^{9})}{b}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

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

$\frac{b (a^{14} \cdot b^{9})}{b^{1}}$

Step 2.2.2.2

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

$\frac{b (a^{14} \cdot b^{9})}{b \cdot 1}$

Step 2.2.2.3

Cancel the common factor.

$\frac{b (a^{14} \cdot b^{9})}{b \cdot 1}$

Step 2.2.2.4

Rewrite the expression.

$\frac{a^{14} \cdot b^{9}}{1}$

Step 2.2.2.5

Divide $a^{14} \cdot b^{9}$ by $1$ .

$a^{14} \cdot b^{9}$

$a^{14} b^{9}$