Write the Fraction in Simplest Form (10p^-2y^5)/(-2(p^4y^2)^4)

$\frac{10 p^{- 2} y^{5}}{- 2 {(p^{4} y^{2})}^{4}}$

Move $p^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{10 y^{5}}{- 2 {(p^{4} y^{2})}^{4} p^{2}}$

Cancel the common factor of $10$ and $- 2$ .

Factor $2$ out of $10 y^{5}$ .

$\frac{2 (5 y^{5})}{- 2 {(p^{4} y^{2})}^{4} p^{2}}$

Cancel the common factors.

Factor $2$ out of $- 2 {(p^{4} y^{2})}^{4} p^{2}$ .

$\frac{2 (5 y^{5})}{2 (- {(p^{4} y^{2})}^{4} p^{2})}$

Cancel the common factor.

$\frac{2 (5 y^{5})}{2 (- {(p^{4} y^{2})}^{4} p^{2})}$

Rewrite the expression.

$\frac{5 y^{5}}{- {(p^{4} y^{2})}^{4} p^{2}}$

Simplify the denominator.

Apply the product rule to $p^{4} y^{2}$ .

$\frac{5 y^{5}}{- {(p^{4})}^{4} {(y^{2})}^{4} p^{2}}$

Multiply the exponents in ${(p^{4})}^{4}$ .

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

$\frac{5 y^{5}}{- p^{4 \cdot 4} {(y^{2})}^{4} p^{2}}$

Multiply $4$ by $4$ .

$\frac{5 y^{5}}{- p^{16} {(y^{2})}^{4} p^{2}}$

Multiply the exponents in ${(y^{2})}^{4}$ .

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

$\frac{5 y^{5}}{- p^{16} y^{2 \cdot 4} p^{2}}$

Multiply $2$ by $4$ .

$\frac{5 y^{5}}{- p^{16} y^{8} p^{2}}$

Multiply $p^{16}$ by $p^{2}$ by adding the exponents.

Move $p^{2}$ .

$\frac{5 y^{5}}{- (p^{2} p^{16}) y^{8}}$

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

$\frac{5 y^{5}}{- p^{2 + 16} y^{8}}$

Add $2$ and $16$ .

$\frac{5 y^{5}}{- p^{18} y^{8}}$

Cancel the common factor of $y^{5}$ and $y^{8}$ .

Factor $y^{5}$ out of $5 y^{5}$ .

$\frac{y^{5} \cdot 5}{- p^{18} y^{8}}$

Cancel the common factors.

Factor $y^{5}$ out of $- p^{18} y^{8}$ .

$\frac{y^{5} \cdot 5}{y^{5} (- p^{18} y^{3})}$

Cancel the common factor.

$\frac{y^{5} \cdot 5}{y^{5} (- p^{18} y^{3})}$

Rewrite the expression.

$\frac{5}{- p^{18} y^{3}}$

Move the negative in front of the fraction.

$- \frac{5}{p^{18} y^{3}}$