Question

Известно, что (2^2+2^2+...+2^2)^2=4^4. Сколько слагаемых в скобке?

Answer 1

4^4=(4^2)^2)=16^2.
Значит, скобка равна 16.
2^2=4; 16=4*4=4*2^2
В скобке 4 слагаемых.

Answer 2

Number of Terms in the Bracket

To determine the number of terms in the given expression, we need to find the number of terms in the bracket (2^2 + 2^2 + ... + 2^2)^2 = 4^4.

The expression inside the bracket is a sum of squares of powers of 2. To find the number of terms, we can look at the pattern of the powers of 2:

2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32

From the pattern, we can see that the powers of 2 increase by 1 each time. So, the number of terms in the bracket is equal to the exponent of the highest power of 2.

In this case, the highest power of 2 is 4, so the number of terms in the bracket is 4.

Therefore, there are 4 terms in the bracket.