Question

There are (43)2⋅ 40 strawberries on a farm. What is the total number of strawberries on the farm?

A: 4^6
B: 4^8
C: 4^9
D: 4^16

Answer 1

To solve the problem, we first need to simplify the expression (43)2⋅ 40.

(43)2 means we should multiply 43 by itself, so:

(43)2 = 43 × 43 = 1849

Now we can substitute this value into the original expression:

(43)2⋅ 40 = 1849 × 40 = 73,960

Therefore, there are 73,960 strawberries on the farm.

To check which answer option is correct, we can convert 73,960 to a power of 4. Since 4^6 = 4 × 4 × 4 × 4 × 4 × 4 = 4^2 × 4^2 × 4^2 = 16 × 16 × 16 = 4,096 and 4^8 = 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 = 4^4 × 4^4 = 256 × 256 = 65,536, we see that the correct answer is not A or B.

Similarly, 4^16 is too large, so the correct answer must be C, 4^9.