Pre-Algebra Examples

$\frac{m^{2} n^{- 5}}{m^{7} n^{- 17}}$

Step 1

Move $n^{- 17}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{m^{2} n^{- 5} n^{17}}{m^{7}}$

Step 2

Multiply $n^{- 5}$ by $n^{17}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $n^{17}$ .

$\frac{m^{2} (n^{17} n^{- 5})}{m^{7}}$

Step 2.2

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

$\frac{m^{2} n^{17 - 5}}{m^{7}}$

Step 2.3

Subtract $5$ from $17$ .

$\frac{m^{2} n^{12}}{m^{7}}$

Step 3

Cancel the common factor of $m^{2}$ and $m^{7}$ .

Tap for more steps...

Step 3.1

Factor $m^{2}$ out of $m^{2} n^{12}$ .

$\frac{m^{2} (n^{12})}{m^{7}}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $m^{2}$ out of $m^{7}$ .

$\frac{m^{2} (n^{12})}{m^{2} m^{5}}$

Step 3.2.2

Cancel the common factor.

$\frac{m^{2} n^{12}}{m^{2} m^{5}}$

Step 3.2.3

Rewrite the expression.

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