Find the Exact Value (2/3)^5*(2/3)^3

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

Step 1

Multiply ${(\frac{2}{3})}^{5}$ by ${(\frac{2}{3})}^{3}$ by adding the exponents.

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

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

Add $5$ and $3$ .

${(\frac{2}{3})}^{8}$

Step 2

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

$\frac{2^{8}}{3^{8}}$

Step 3

Raise $2$ to the power of $8$ .

$\frac{256}{3^{8}}$

Step 4

Raise $3$ to the power of $8$ .

$\frac{256}{6561}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{256}{6561}$

Decimal Form:

$0.03901844 \dots$