Simplify ((b^-3c^4)/(b^-6))^4

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

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

${(b^{- 3} c^{4} b^{6})}^{4}$

Multiply $b^{- 3}$ by $b^{6}$ by adding the exponents.

Move $b^{6}$ .

${(b^{6} b^{- 3} c^{4})}^{4}$

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

${(b^{6 - 3} c^{4})}^{4}$

Subtract $3$ from $6$ .

${(b^{3} c^{4})}^{4}$

Apply the product rule to $b^{3} c^{4}$ .

${(b^{3})}^{4} {(c^{4})}^{4}$

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

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

$b^{3 \cdot 4} {(c^{4})}^{4}$

Multiply $3$ by $4$ .

$b^{12} {(c^{4})}^{4}$

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

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

$b^{12} c^{4 \cdot 4}$

Multiply $4$ by $4$ .

$b^{12} c^{16}$