Simplify (4^2m^6t^8)/(4^6m^9t^-6)

$\frac{4^{2} m^{6} t^{8}}{4^{6} m^{9} t^{- 6}}$

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

$\frac{4^{2} m^{6} t^{8} t^{6}}{4^{6} m^{9}}$

Multiply $t^{8}$ by $t^{6}$ by adding the exponents.

Move $t^{6}$ .

$\frac{4^{2} m^{6} (t^{6} t^{8})}{4^{6} m^{9}}$

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

$\frac{4^{2} m^{6} t^{6 + 8}}{4^{6} m^{9}}$

Add $6$ and $8$ .

$\frac{4^{2} m^{6} t^{14}}{4^{6} m^{9}}$

Cancel the common factor of $4^{2}$ and $4^{6}$ .

Factor $4^{2}$ out of $4^{2} m^{6} t^{14}$ .

$\frac{4^{2} (m^{6} t^{14})}{4^{6} m^{9}}$

Cancel the common factors.

Factor $4^{2}$ out of $4^{6} m^{9}$ .

$\frac{4^{2} (m^{6} t^{14})}{4^{2} (4^{4} m^{9})}$

Cancel the common factor.

$\frac{4^{2} (m^{6} t^{14})}{4^{2} (4^{4} m^{9})}$

Rewrite the expression.

$\frac{m^{6} t^{14}}{4^{4} m^{9}}$

Cancel the common factor of $m^{6}$ and $m^{9}$ .

Factor $m^{6}$ out of $m^{6} t^{14}$ .

$\frac{m^{6} (t^{14})}{4^{4} m^{9}}$

Cancel the common factors.

Factor $m^{6}$ out of $4^{4} m^{9}$ .

$\frac{m^{6} (t^{14})}{m^{6} (4^{4} m^{3})}$

Cancel the common factor.

$\frac{m^{6} t^{14}}{m^{6} (4^{4} m^{3})}$

Rewrite the expression.

$\frac{t^{14}}{4^{4} m^{3}}$

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

$\frac{t^{14}}{256 m^{3}}$