Question

(2 2/3)^5 • (3/8)^6=?^-степеть​

Answer 1

Ответ:

3/8

Объяснение:

(8/3)⁵ × (3/8)⁶= (8/3)⁵×(8/3)^-6= (8/3)^-1= 3/8

Answer 2

To simplify the expression $(2 \frac{2}{3})^5 \cdot (\frac{3}{8})^6$, we'll break it down step by step:

Step 1: Convert the mixed number $2 \frac{2}{3}$ into an improper fraction.

$$2 \frac{2}{3} = \frac{(2 \times 3) + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}$$

Step 2: Simplify the exponents.

$$\begin{align*} (2 \frac{2}{3})^5 \cdot (\frac{3}{8})^6 &= \left(\frac{8}{3}\right)^5 \cdot \left(\frac{3}{8}\right)^6 \\ &= \frac{8^5}{3^5} \cdot \frac{3^6}{8^6} \end{align*}$$

Step 3: Simplify each fraction separately.

$$\begin{align*} \frac{8^5}{3^5} &= \frac{32768}{243} \\ \frac{3^6}{8^6} &= \frac{729}{262144} \end{align*}$$

Step 4: Multiply the simplified fractions.

$$\frac{32768}{243} \cdot \frac{729}{262144} = \frac{23914897}{158203456}$$

Therefore, $(2 \frac{2}{3})^5 \cdot (\frac{3}{8})^6$ simplifies to $\frac{23914897}{158203456}$ or approximately $0.15133817$.