Precalculus Examples

$\frac{{(b^{n})}^{3}}{b^{n} \cdot b^{n}}$

Step 1

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

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Step 1.1

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

$\frac{{(b^{n})}^{3}}{b^{n + n}}$

Step 1.2

Add $n$ and $n$ .

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

Step 2

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

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Step 2.1

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

$\frac{b^{n \cdot 3}}{b^{2 n}}$

Step 2.2

Move $3$ to the left of $n$ .

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

Step 3

Cancel the common factor of $b^{3 n}$ and $b^{2 n}$ .

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Step 3.1

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

$\frac{b^{2 n} b^{n}}{b^{2 n}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{b^{2 n} b^{n}}{b^{2 n} \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{b^{2 n} b^{n}}{b^{2 n} \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{b^{n}}{1}$

Step 3.2.4

Divide $b^{n}$ by $1$ .

$b^{n}$