Write the Fraction in Simplest Form (-3(t)^2)/(-12t^-4)

$\frac{- 3 {(t)}^{2}}{- 12 t^{- 4}}$

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

$\frac{- 3 {(t)}^{2} t^{4}}{- 12}$

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

Move $t^{4}$ .

$\frac{- 3 (t^{4} {(t)}^{2})}{- 12}$

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

$\frac{- 3 t^{4 + 2}}{- 12}$

Add $4$ and $2$ .

$\frac{- 3 t^{6}}{- 12}$

Cancel the common factor of $- 3$ and $- 12$ .

Factor $- 3$ out of $- 3 t^{6}$ .

$\frac{- 3 (t^{6})}{- 12}$

Cancel the common factors.

Factor $- 3$ out of $- 12$ .

$\frac{- 3 (t^{6})}{- 3 (4)}$

Cancel the common factor.

$\frac{- 3 t^{6}}{- 3 \cdot 4}$

Rewrite the expression.

$\frac{t^{6}}{4}$