Pre-Algebra Examples

$\frac{{(m^{2})}^{6} m}{m^{6}}$

Step 1

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

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Step 1.1

Factor $m$ out of ${(m^{2})}^{6} m$ .

$\frac{m {(m^{2})}^{6}}{m^{6}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $m$ out of $m^{6}$ .

$\frac{m {(m^{2})}^{6}}{m \cdot m^{5}}$

Step 1.2.2

Cancel the common factor.

$\frac{m {(m^{2})}^{6}}{m \cdot m^{5}}$

Step 1.2.3

Rewrite the expression.

$\frac{{(m^{2})}^{6}}{m^{5}}$

Step 2

Multiply the exponents in ${(m^{2})}^{6}$ .

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Step 2.1

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

$\frac{m^{2 \cdot 6}}{m^{5}}$

Step 2.2

Multiply $2$ by $6$ .

$\frac{m^{12}}{m^{5}}$

Step 3

Cancel the common factor of $m^{12}$ and $m^{5}$ .

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Step 3.1

Factor $m^{5}$ out of $m^{12}$ .

$\frac{m^{5} m^{7}}{m^{5}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{m^{5} m^{7}}{m^{5} \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{m^{5} m^{7}}{m^{5} \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{m^{7}}{1}$

Step 3.2.4

Divide $m^{7}$ by $1$ .

$m^{7}$