Simplify -(5t^5)/((5t^4)^2)

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

Simplify the denominator.

Apply the product rule to $5 t^{4}$ .

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

Raise $5$ to the power of $2$ .

$- \frac{5 t^{5}}{25 {(t^{4})}^{2}}$

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

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

$- \frac{5 t^{5}}{25 t^{4 \cdot 2}}$

Multiply $4$ by $2$ .

$- \frac{5 t^{5}}{25 t^{8}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $5$ and $25$ .

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

$- \frac{5 (t^{5})}{25 t^{8}}$

Cancel the common factors.

Factor $5$ out of $25 t^{8}$ .

$- \frac{5 (t^{5})}{5 (5 t^{8})}$

Cancel the common factor.

$- \frac{5 t^{5}}{5 (5 t^{8})}$

Rewrite the expression.

$- \frac{t^{5}}{5 t^{8}}$

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

Multiply by $1$ .

$- \frac{t^{5} \cdot 1}{5 t^{8}}$

Cancel the common factors.

Factor $t^{5}$ out of $5 t^{8}$ .

$- \frac{t^{5} \cdot 1}{t^{5} (5 t^{3})}$

Cancel the common factor.

$- \frac{t^{5} \cdot 1}{t^{5} (5 t^{3})}$

Rewrite the expression.

$- \frac{1}{5 t^{3}}$