Simplify 2/((16m^3n^4)^-3)

$\frac{2}{{(16 m^{3} n^{4})}^{- 3}}$

Move ${(16 m^{3} n^{4})}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$2 {(16 m^{3} n^{4})}^{3}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $16 m^{3} n^{4}$ .

$2 ({(16 m^{3})}^{3} {(n^{4})}^{3})$

Apply the product rule to $16 m^{3}$ .

$2 (16^{3} {(m^{3})}^{3} {(n^{4})}^{3})$

Raise $16$ to the power of $3$ .

$2 (4096 {(m^{3})}^{3} {(n^{4})}^{3})$

Multiply the exponents in ${(m^{3})}^{3}$ .

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

$2 (4096 m^{3 \cdot 3} {(n^{4})}^{3})$

Multiply $3$ by $3$ .

$2 (4096 m^{9} {(n^{4})}^{3})$

Multiply the exponents in ${(n^{4})}^{3}$ .

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

$2 (4096 m^{9} n^{4 \cdot 3})$

Multiply $4$ by $3$ .

$2 (4096 m^{9} n^{12})$

Multiply $4096$ by $2$ .

$8192 m^{9} n^{12}$