Simplify ((2x^3)/(x^32x^22x^4))^4

${(\frac{2 x^{3}}{x^{3} \cdot 2 x^{2} \cdot 2 x^{4}})}^{4}$

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

${(\frac{2 x^{3}}{x^{2} x^{3} \cdot 2 \cdot (2 x^{4})})}^{4}$

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

${(\frac{2 x^{3}}{x^{2 + 3} \cdot 2 \cdot (2 x^{4})})}^{4}$

Add $2$ and $3$ .

${(\frac{2 x^{3}}{x^{5} \cdot 2 \cdot (2 x^{4})})}^{4}$

Multiply $x^{5}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

${(\frac{2 x^{3}}{x^{4} x^{5} \cdot 2 \cdot 2})}^{4}$

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

${(\frac{2 x^{3}}{x^{4 + 5} \cdot 2 \cdot 2})}^{4}$

Add $4$ and $5$ .

${(\frac{2 x^{3}}{x^{9} \cdot 2 \cdot 2})}^{4}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{2 x^{3}}{x^{9} \cdot 2 \cdot 2})}^{4}$

Rewrite the expression.

${(\frac{x^{3}}{x^{9} \cdot 2})}^{4}$

Cancel the common factor of $x^{3}$ and $x^{9}$ .

Multiply by $1$ .

${(\frac{x^{3} \cdot 1}{x^{9} \cdot 2})}^{4}$

Cancel the common factors.

Factor $x^{3}$ out of $x^{9} \cdot 2$ .

${(\frac{x^{3} \cdot 1}{x^{3} (x^{6} \cdot 2)})}^{4}$

Cancel the common factor.

${(\frac{x^{3} \cdot 1}{x^{3} (x^{6} \cdot 2)})}^{4}$

Rewrite the expression.

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

Move $2$ to the left of $x^{6}$ .

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

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

Apply the product rule to $\frac{1}{2 x^{6}}$ .

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

Apply the product rule to $2 x^{6}$ .

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

One to any power is one.

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

Simplify the denominator.

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

$\frac{1}{16 {(x^{6})}^{4}}$

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

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

$\frac{1}{16 x^{6 \cdot 4}}$

Multiply $6$ by $4$ .

$\frac{1}{16 x^{24}}$

Simplify ((2x^3)/(x^3*2x^2*2x^4))^4

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Simplify ((2x^3)/(x^32x^22x^4))^4