Evaluate (45m^-6p^2v^12)/(15m^-2p^8v^-4)

$\frac{45 m^{- 6} p^{2} v^{12}}{15 m^{- 2} p^{8} v^{- 4}}$

Step 1

Move $m^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{45 p^{2} v^{12}}{15 m^{- 2} p^{8} v^{- 4} m^{6}}$

Step 2

Multiply $m^{- 2}$ by $m^{6}$ by adding the exponents.

Move $m^{6}$ .

$\frac{45 p^{2} v^{12}}{15 (m^{6} m^{- 2}) p^{8} v^{- 4}}$

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

$\frac{45 p^{2} v^{12}}{15 m^{6 - 2} p^{8} v^{- 4}}$

Subtract $2$ from $6$ .

$\frac{45 p^{2} v^{12}}{15 m^{4} p^{8} v^{- 4}}$

Step 3

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

$\frac{45 p^{2} v^{12} v^{4}}{15 m^{4} p^{8}}$

Step 4

Multiply $v^{12}$ by $v^{4}$ by adding the exponents.

Move $v^{4}$ .

$\frac{45 p^{2} (v^{4} v^{12})}{15 m^{4} p^{8}}$

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

$\frac{45 p^{2} v^{4 + 12}}{15 m^{4} p^{8}}$

Add $4$ and $12$ .

$\frac{45 p^{2} v^{16}}{15 m^{4} p^{8}}$

Step 5

Cancel the common factor of $45$ and $15$ .

Factor $15$ out of $45 p^{2} v^{16}$ .

$\frac{15 (3 p^{2} v^{16})}{15 m^{4} p^{8}}$

Cancel the common factors.

Factor $15$ out of $15 m^{4} p^{8}$ .

$\frac{15 (3 p^{2} v^{16})}{15 (m^{4} p^{8})}$

Cancel the common factor.

$\frac{15 (3 p^{2} v^{16})}{15 (m^{4} p^{8})}$

Rewrite the expression.

$\frac{3 p^{2} v^{16}}{m^{4} p^{8}}$

Step 6

Cancel the common factor of $p^{2}$ and $p^{8}$ .

Factor $p^{2}$ out of $3 p^{2} v^{16}$ .

$\frac{p^{2} (3 v^{16})}{m^{4} p^{8}}$

Cancel the common factors.

Factor $p^{2}$ out of $m^{4} p^{8}$ .

$\frac{p^{2} (3 v^{16})}{p^{2} (m^{4} p^{6})}$

Cancel the common factor.

$\frac{p^{2} (3 v^{16})}{p^{2} (m^{4} p^{6})}$

Rewrite the expression.

$\frac{3 v^{16}}{m^{4} p^{6}}$