Final answer:
To simplify the given expression, combine the like terms in the numerator and the denominator. Then, divide the numerator by the denominator to get the final answer of 1.
Step-by-step explanation:
To simplify the given expression, we need to follow the rules of exponentiation. We can start by combining the like terms in the numerator and the denominator separately. In the numerator, we have 2^2 * 2^5, which can be simplified as 2^(2+5) = 2^7. In the denominator, we have 2^5 * 2^2, which can be simplified as 2^(5+2) = 2^7. Therefore, the expression becomes 2^7 / 2^7.
Now, we can simplify the numerator and denominator further. When we divide two terms with the same base and different exponents, we subtract the exponents. Therefore, 2^7 / 2^7 = 2^(7-7) = 2^0.
Any number raised to the power of 0 is equal to 1. Therefore, 2^0 = 1. So the simplified expression is 1.
To simplify the expression 2^2*1/2^5*2^5*1/2^2, we can apply the rules of exponents. For multiplication, we add the exponents if the bases are the same, and for division, we subtract the exponents. Therefore:
We first simplify 2^2 * 2^5 to 2^(2+5), which equals 2^7.
Next, we simplify 1/2^5 * 1/2^2 to 1/2^(5+2), which equals 1/2^7.
Now, we simplify 2^7 * 1/2^7 to 2^(7-7), which equals 2^0.
Any number raised to the power of 0 equals 1. Therefore, 2^0 is simply 1.
The final answer is 1.