Simplify ((2x^7)/(y^4))^-6

${(\frac{2 x^{7}}{y^{4}})}^{- 6}$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{y^{4}}{2 x^{7}})}^{6}$

Step 2

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

Apply the product rule to $\frac{y^{4}}{2 x^{7}}$ .

$\frac{{(y^{4})}^{6}}{{(2 x^{7})}^{6}}$

Apply the product rule to $2 x^{7}$ .

$\frac{{(y^{4})}^{6}}{2^{6} {(x^{7})}^{6}}$

Step 3

Multiply the exponents in ${(y^{4})}^{6}$ .

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

$\frac{y^{4 \cdot 6}}{2^{6} {(x^{7})}^{6}}$

Multiply $4$ by $6$ .

$\frac{y^{24}}{2^{6} {(x^{7})}^{6}}$

Step 4

Simplify the denominator.

Raise $2$ to the power of $6$ .

$\frac{y^{24}}{64 {(x^{7})}^{6}}$

Multiply the exponents in ${(x^{7})}^{6}$ .

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

$\frac{y^{24}}{64 x^{7 \cdot 6}}$

Multiply $7$ by $6$ .

$\frac{y^{24}}{64 x^{42}}$