Simplify ((3e^3)/(6e^2))^2

${(\frac{3 e^{3}}{6 e^{2}})}^{2}$

Step 1

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3 e^{3}$ .

${(\frac{3 (e^{3})}{6 e^{2}})}^{2}$

Cancel the common factors.

Factor $3$ out of $6 e^{2}$ .

${(\frac{3 (e^{3})}{3 (2 e^{2})})}^{2}$

Cancel the common factor.

${(\frac{3 e^{3}}{3 (2 e^{2})})}^{2}$

Rewrite the expression.

${(\frac{e^{3}}{2 e^{2}})}^{2}$

${(\frac{e^{3}}{2 e^{2}})}^{2}$

${(\frac{e^{3}}{2 e^{2}})}^{2}$

Step 2

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

Factor $e^{2}$ out of $e^{3}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 3

Simplify the expression.

Apply the product rule to $\frac{e}{2}$ .

$\frac{e^{2}}{2^{2}}$

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

$\frac{e^{2}}{4}$

$\frac{e^{2}}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{e^{2}}{4}$

Decimal Form:

$1.84726402 \dots$

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