Simplify (-10m^-1y^0r)/(-14m^-7y^-3r^-4)

$\frac{- 10 m^{- 1} y^{0} r}{- 14 m^{- 7} y^{- 3} r^{- 4}}$

Step 1

Move $m^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 10 m^{- 1} y^{0} r m^{7}}{- 14 y^{- 3} r^{- 4}}$

Step 2

Move $y^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 10 m^{- 1} y^{0} r m^{7} y^{3}}{- 14 r^{- 4}}$

Step 3

Move $r^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 10 m^{- 1} y^{0} r m^{7} y^{3} r^{4}}{- 14}$

Step 4

Simplify the numerator.

Multiply $m^{- 1}$ by $m^{7}$ by adding the exponents.

Move $m^{7}$ .

$\frac{- 10 (m^{7} m^{- 1}) y^{0} r y^{3} r^{4}}{- 14}$

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

$\frac{- 10 m^{7 - 1} y^{0} r y^{3} r^{4}}{- 14}$

Subtract $1$ from $7$ .

$\frac{- 10 m^{6} y^{0} r y^{3} r^{4}}{- 14}$

Simplify $- 10 m^{6} y^{0} r$ .

$\frac{- 10 m^{6} r y^{3} r^{4}}{- 14}$

Multiply $r$ by $r^{4}$ by adding the exponents.

Move $r^{4}$ .

$\frac{- 10 m^{6} (r^{4} r) y^{3}}{- 14}$

Multiply $r^{4}$ by $r$ .

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

$\frac{- 10 m^{6} (r^{4} r^{1}) y^{3}}{- 14}$

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

$\frac{- 10 m^{6} r^{4 + 1} y^{3}}{- 14}$

Add $4$ and $1$ .

$\frac{- 10 m^{6} r^{5} y^{3}}{- 14}$

Step 5

Cancel the common factor of $- 10$ and $- 14$ .

Factor $- 2$ out of $- 10 m^{6} r^{5} y^{3}$ .

$\frac{- 2 (5 m^{6} r^{5} y^{3})}{- 14}$

Cancel the common factors.

Factor $- 2$ out of $- 14$ .

$\frac{- 2 (5 m^{6} r^{5} y^{3})}{- 2 (7)}$

Cancel the common factor.

$\frac{- 2 (5 m^{6} r^{5} y^{3})}{- 2 \cdot 7}$

Rewrite the expression.

$\frac{5 m^{6} r^{5} y^{3}}{7}$