Simplify ((a^4x^y)/(c^(k-2)))^b

${(\frac{a^{4} x^{y}}{c^{k - 2}})}^{b}$

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

Apply the product rule to $\frac{a^{4} x^{y}}{c^{k - 2}}$ .

$\frac{{(a^{4} x^{y})}^{b}}{{(c^{k - 2})}^{b}}$

Apply the product rule to $a^{4} x^{y}$ .

$\frac{{(a^{4})}^{b} {(x^{y})}^{b}}{{(c^{k - 2})}^{b}}$

Simplify the numerator.

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

$\frac{a^{4 b} {(x^{y})}^{b}}{{(c^{k - 2})}^{b}}$

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

$\frac{a^{4 b} x^{y b}}{{(c^{k - 2})}^{b}}$

Multiply the exponents in ${(c^{k - 2})}^{b}$ .

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

$\frac{a^{4 b} x^{y b}}{c^{(k - 2) b}}$

Apply the distributive property.

$\frac{a^{4 b} x^{y b}}{c^{k b - 2 b}}$