Basic Math Examples

$n^{6} \cdot n^{5} \div n^{4} \cdot n^{3} \div n^{2} \cdot n$

Step 1

Multiply $n^{6}$ by $n^{5}$ 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.

$n^{6 + 5} \div n^{4} \cdot n^{3} \div n^{2} \cdot n$

Step 1.2

Add $6$ and $5$ .

$n^{11} \div n^{4} \cdot n^{3} \div n^{2} \cdot n$

Step 2

Combine $n^{11} \div n^{4}$ and $n^{3}$ .

$\frac{n^{11} n^{3}}{n^{4}} \div n^{2} \cdot n$

Step 3

Multiply $n^{11}$ by $n^{3}$ by adding the exponents.

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Step 3.1

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

$\frac{n^{11 + 3}}{n^{4}} \div n^{2} \cdot n$

Step 3.2

Add $11$ and $3$ .

$\frac{n^{14}}{n^{4}} \div n^{2} \cdot n$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Reduce the expression $\frac{n^{14}}{n^{4}}$ by cancelling the common factors.

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Step 4.1.1

Factor $n^{4}$ out of $n^{14}$ .

$\frac{n^{4} n^{10}}{n^{4}} \div n^{2} \cdot n$

Step 4.1.2

Multiply by $1$ .

$\frac{n^{4} n^{10}}{n^{4} \cdot 1} \div n^{2} \cdot n$

Step 4.1.3

Cancel the common factor.

$\frac{n^{4} n^{10}}{n^{4} \cdot 1} \div n^{2} \cdot n$

Step 4.1.4

Rewrite the expression.

$\frac{n^{10}}{1} \div n^{2} \cdot n$

Step 4.2

Divide $n^{10}$ by $1$ .

$n^{10} \div n^{2} \cdot n$

Step 5

Rewrite the division as a fraction.

$\frac{n^{10}}{n^{2}} \cdot n$

Step 6

Cancel the common factor of $n$ .

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Step 6.1

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

$\frac{n^{10}}{n \cdot n} \cdot n$

Step 6.2

Cancel the common factor.

$\frac{n^{10}}{n \cdot n} \cdot n$

Step 6.3

Rewrite the expression.

$\frac{n^{10}}{n}$

Step 7

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

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Step 7.1

Factor $n$ out of $n^{10}$ .

$\frac{n \cdot n^{9}}{n}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

$\frac{n \cdot n^{9}}{n^{1}}$

Step 7.2.2

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

$\frac{n \cdot n^{9}}{n \cdot 1}$

Step 7.2.3

Cancel the common factor.

$\frac{n \cdot n^{9}}{n \cdot 1}$

Step 7.2.4

Rewrite the expression.

$\frac{n^{9}}{1}$

Step 7.2.5

Divide $n^{9}$ by $1$ .

$n^{9}$