Simplify ((d^2)/(e^(2/3)))^(2/5)

${(\frac{d^{2}}{e^{\frac{2}{3}}})}^{\frac{2}{5}}$

Step 1

Apply the product rule to $\frac{d^{2}}{e^{\frac{2}{3}}}$ .

$\frac{{(d^{2})}^{\frac{2}{5}}}{{(e^{\frac{2}{3}})}^{\frac{2}{5}}}$

Step 2

Multiply the exponents in ${(d^{2})}^{\frac{2}{5}}$ .

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

$\frac{d^{2 (\frac{2}{5})}}{{(e^{\frac{2}{3}})}^{\frac{2}{5}}}$

Multiply $2 (\frac{2}{5})$ .

Combine $2$ and $\frac{2}{5}$ .

$\frac{d^{\frac{2 \cdot 2}{5}}}{{(e^{\frac{2}{3}})}^{\frac{2}{5}}}$

Multiply $2$ by $2$ .

$\frac{d^{\frac{4}{5}}}{{(e^{\frac{2}{3}})}^{\frac{2}{5}}}$

Step 3

Multiply the exponents in ${(e^{\frac{2}{3}})}^{\frac{2}{5}}$ .

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

$\frac{d^{\frac{4}{5}}}{e^{\frac{2}{3} \cdot \frac{2}{5}}}$

Multiply $\frac{2}{3} \cdot \frac{2}{5}$ .

Multiply $\frac{2}{3}$ by $\frac{2}{5}$ .

$\frac{d^{\frac{4}{5}}}{e^{\frac{2 \cdot 2}{3 \cdot 5}}}$

Multiply $2$ by $2$ .

$\frac{d^{\frac{4}{5}}}{e^{\frac{4}{3 \cdot 5}}}$

Multiply $3$ by $5$ .

$\frac{d^{\frac{4}{5}}}{e^{\frac{4}{15}}}$