Simplify (7(e^(3x))^2)/(14e^x)

$\frac{7 {(e^{3 x})}^{2}}{14 e^{x}}$

Step 1

Cancel the common factor of $7$ and $14$ .

Factor $7$ out of $7 {(e^{3 x})}^{2}$ .

$\frac{7 ({(e^{3 x})}^{2})}{14 e^{x}}$

Cancel the common factors.

Factor $7$ out of $14 e^{x}$ .

$\frac{7 ({(e^{3 x})}^{2})}{7 (2 e^{x})}$

Cancel the common factor.

$\frac{7 {(e^{3 x})}^{2}}{7 (2 e^{x})}$

Rewrite the expression.

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

Step 2

Multiply the exponents in ${(e^{3 x})}^{2}$ .

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

$\frac{e^{3 x \cdot 2}}{2 e^{x}}$

Multiply $2$ by $3$ .

$\frac{e^{6 x}}{2 e^{x}}$

Step 3

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

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

$\frac{e^{x} e^{5 x}}{2 e^{x}}$

Cancel the common factors.

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

$\frac{e^{x} e^{5 x}}{e^{x} \cdot 2}$

Cancel the common factor.

$\frac{e^{x} e^{5 x}}{e^{x} \cdot 2}$

Rewrite the expression.

$\frac{e^{5 x}}{2}$