Simplify (12x^-5y^9)/(2x^-10y^m)

$\frac{12 x^{- 5} y^{9}}{2 x^{- 10} y^{m}}$

Step 1

Move $x^{- 10}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{12 x^{- 5} y^{9} x^{10}}{2 y^{m}}$

Step 2

Multiply $x^{- 5}$ by $x^{10}$ by adding the exponents.

Move $x^{10}$ .

$\frac{12 (x^{10} x^{- 5}) y^{9}}{2 y^{m}}$

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

$\frac{12 x^{10 - 5} y^{9}}{2 y^{m}}$

Subtract $5$ from $10$ .

$\frac{12 x^{5} y^{9}}{2 y^{m}}$

Step 3

Cancel the common factor of $12$ and $2$ .

Factor $2$ out of $12 x^{5} y^{9}$ .

$\frac{2 (6 x^{5} y^{9})}{2 y^{m}}$

Cancel the common factors.

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

$\frac{2 (6 x^{5} y^{9})}{2 (y^{m})}$

Cancel the common factor.

$\frac{2 (6 x^{5} y^{9})}{2 y^{m}}$

Rewrite the expression.

$\frac{6 x^{5} y^{9}}{y^{m}}$

Step 4

Cancel the common factor of $y^{9}$ and $y^{m}$ .

Factor $y^{m}$ out of $6 x^{5} y^{9}$ .

$\frac{y^{m} (6 x^{5} y^{9 - m})}{y^{m}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{y^{m} (6 x^{5} y^{9 - m})}{y^{m} \cdot 1}$

Cancel the common factor.

$\frac{y^{m} (6 x^{5} y^{9 - m})}{y^{m} \cdot 1}$

Rewrite the expression.

$\frac{6 x^{5} y^{9 - m}}{1}$

Divide $6 x^{5} y^{9 - m}$ by $1$ .

$6 x^{5} y^{9 - m}$