Simplify ((4x^8)/(2x^6))^4

${(\frac{4 x^{8}}{2 x^{6}})}^{4}$

Step 1

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 x^{8}$ .

${(\frac{2 (2 x^{8})}{2 x^{6}})}^{4}$

Cancel the common factors.

Factor $2$ out of $2 x^{6}$ .

${(\frac{2 (2 x^{8})}{2 (x^{6})})}^{4}$

Cancel the common factor.

${(\frac{2 (2 x^{8})}{2 x^{6}})}^{4}$

Rewrite the expression.

${(\frac{2 x^{8}}{x^{6}})}^{4}$

${(\frac{2 x^{8}}{x^{6}})}^{4}$

${(\frac{2 x^{8}}{x^{6}})}^{4}$

Step 2

Cancel the common factor of $x^{8}$ and $x^{6}$ .

Factor $x^{6}$ out of $2 x^{8}$ .

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

Cancel the common factors.

Multiply by $1$ .

${(\frac{x^{6} (2 x^{2})}{x^{6} \cdot 1})}^{4}$

Cancel the common factor.

${(\frac{x^{6} (2 x^{2})}{x^{6} \cdot 1})}^{4}$

Rewrite the expression.

${(\frac{2 x^{2}}{1})}^{4}$

Divide $2 x^{2}$ by $1$ .

${(2 x^{2})}^{4}$

${(2 x^{2})}^{4}$

${(2 x^{2})}^{4}$

Step 3

Simplify the expression.

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

$2^{4} {(x^{2})}^{4}$

Raise $2$ to the power of $4$ .

$16 {(x^{2})}^{4}$

Multiply the exponents in ${(x^{2})}^{4}$ .

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

$16 x^{2 \cdot 4}$

Multiply $2$ by $4$ .

$16 x^{8}$

$16 x^{8}$

$16 x^{8}$

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