Write the Fraction in Simplest Form (3m^8)/((4mt^-2)^2)

$\frac{3 m^{8}}{{(4 m t^{- 2})}^{2}}$

Simplify the denominator.

Apply the product rule to $4 m t^{- 2}$ .

$\frac{3 m^{8}}{{(4 m)}^{2} {(t^{- 2})}^{2}}$

Apply the product rule to $4 m$ .

$\frac{3 m^{8}}{4^{2} m^{2} {(t^{- 2})}^{2}}$

Raise $4$ to the power of $2$ .

$\frac{3 m^{8}}{16 m^{2} {(t^{- 2})}^{2}}$

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

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

$\frac{3 m^{8}}{16 m^{2} t^{- 2 \cdot 2}}$

Multiply $- 2$ by $2$ .

$\frac{3 m^{8}}{16 m^{2} t^{- 4}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3 m^{8}}{16 m^{2} \frac{1}{t^{4}}}$

Combine exponents.

Combine $16$ and $\frac{1}{t^{4}}$ .

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

Combine $m^{2}$ and $\frac{16}{t^{4}}$ .

$\frac{3 m^{8}}{\frac{m^{2} \cdot 16}{t^{4}}}$

Move $16$ to the left of $m^{2}$ .

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

Multiply the numerator by the reciprocal of the denominator.

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

Cancel the common factor of $m^{2}$ .

Factor $m^{2}$ out of $3 m^{8}$ .

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

Factor $m^{2}$ out of $16 m^{2}$ .

$m^{2} (3 m^{6}) \frac{t^{4}}{m^{2} \cdot 16}$

Cancel the common factor.

$m^{2} (3 m^{6}) \frac{t^{4}}{m^{2} \cdot 16}$

Rewrite the expression.

$3 m^{6} \frac{t^{4}}{16}$

Combine $3$ and $\frac{t^{4}}{16}$ .

$m^{6} \frac{3 t^{4}}{16}$

Combine $m^{6}$ and $\frac{3 t^{4}}{16}$ .

$\frac{m^{6} (3 t^{4})}{16}$

Move $3$ to the left of $m^{6}$ .

$\frac{3 m^{6} t^{4}}{16}$