Evaluate ((2^24^2)/(42^3))^2

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

Cancel the common factor of $2^{2}$ and $2^{3}$ .

Factor $2^{2}$ out of $2^{2} \cdot 4^{2}$ .

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

Cancel the common factors.

Factor $2^{2}$ out of $4 \cdot 2^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Cancel the common factor of $4^{2}$ and $4$ .

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

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

Cancel the common factors.

Factor $4$ out of $4 \cdot 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Factor $2$ out of $4$ .

${(\frac{2 \cdot 2}{2})}^{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

${(\frac{2 \cdot 2}{2 (1)})}^{2}$

Cancel the common factor.

${(\frac{2 \cdot 2}{2 \cdot 1})}^{2}$

Rewrite the expression.

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

Divide $2$ by $1$ .

$2^{2}$

$2^{2}$

$2^{2}$

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

$4$

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