2^100+2^100 is the answer 4^200
what is this: ^??
thats and 2 to the 100 power
then no that is not the answer. 2 to the 100th power is 1.2676506 × 10^30. now multiply that by 2
If you have x^2 + x^2, you can add the coefficients to get 2*x^2
So 2^100 + 2^100 = 2(2^100)
= 2^1 * 2^100
You can add the exponents when multiplying.
= 2^101
To determine if the expression 2^100 + 2^100 equals 4^200, we need to evaluate both sides of the equation.
First, let's simplify the left side of the equation:
2^100 + 2^100 = (2 + 2) ^ 100 (using the exponentiation rule: a^n + b^n = (a + b) ^ n)
Simplifying further:
(2 + 2) ^ 100 = 4 ^ 100
Now, let's compare this result to the right side of the equation:
4 ^ 200
To see if they are equal, we need to simplify both sides to a common form.
Since 100 is half of 200, we can rewrite the right side of the equation as:
4 ^ 200 = (2 ^ 2) ^ 100 (using the exponentiation rule: (a ^ m) ^ n = a ^ (m * n))
Simplifying further:
(2 ^ 2) ^ 100 = 2 ^ (2 * 100) = 2 ^ 200
Now we can compare the two sides of the equation:
4 ^ 100 versus 2 ^ 200
Although the bases are different, 4 ^ 100 can be rewritten as (2 ^ 2) ^ 100, which equals 2 ^ 200.
Therefore, we can conclude that 2^100 + 2^100 is indeed equal to 4^200.