Give your answer correct to two dedimel places. $$ 5(3.14)^{2}\left(\frac{2}{3}\right)^{4} $$ $$ \frac{1}{4} $$

Question

UpStudy AI · Accepted Answer

To solve the expression $$ 5(3.14)^{2}\left(\frac{2}{3}\right)^{4} $$ and then divide it by $$ \frac{1}{4} $$, we will follow these steps:

1. Calculate $$ (3.14)^{2} $$:
   $$
   (3.14)^{2} = 3.14 \times 3.14 = 9.8596
   $$

2. Calculate $$ \left(\frac{2}{3}\right)^{4} $$:
   $$
   \left(\frac{2}{3}\right)^{4} = \frac{2^4}{3^4} = \frac{16}{81}
   $$

3. Now, substitute these values into the expression:
   $$
   5(3.14)^{2}\left(\frac{2}{3}\right)^{4} = 5 \times 9.8596 \times \frac{16}{81}
   $$

4. Calculate $$ 5 \times 9.8596 $$:
   $$
   5 \times 9.8596 = 49.298
   $$

5. Now multiply by $$ \frac{16}{81} $$:
   $$
   49.298 \times \frac{16}{81} = \frac{49.298 \times 16}{81}
   $$

6. Calculate $$ 49.298 \times 16 $$:
   $$
   49.298 \times 16 = 788.768
   $$

7. Now divide by $$ 81 $$:
   $$
   \frac{788.768}{81} \approx 9.733
   $$

8. Finally, divide by $$ \frac{1}{4} $$ (which is the same as multiplying by 4):
   $$
   9.733 \times 4 = 38.932
   $$

Now, rounding to two decimal places:
$$
\boxed{38.93}
$$
The result is 38.93.

Give your answer correct to two dedimel places. \( 5(3.14)^{2}\left(\frac{2}{3}\right)^{4} \) \( \frac{1}{4} \)