Using the Product Rule of Exponents, what is the exponent of (1/2) to the 2 power times (1/2) to the 2 power; 2 in exponential simplest form?
Applying the Product Rule of Exponents, we add the exponents when multiplying powers with the same base.
Thus, we have:
(1/2)^2 * (1/2)^2 = (1/2)^(2+2) = (1/2)^4 = 1/(2^4) = 1/16
So, the exponential simplest form is 1/16.
To simplify the expression (1/2)^2 * (1/2)^2, we can use the product rule of exponents, which states that for any non-zero number x and any integers m and n:
x^m * x^n = x^(m+n)
Applying this rule to the given expression, we have:
(1/2)^2 * (1/2)^2 = 1/2^(2+2)
Simplifying the exponent inside the parentheses:
= 1/2^4
Since 2^4 = 2 * 2 * 2 * 2 = 16, we can write:
= 1/16
Therefore, the expression (1/2)^2 * (1/2)^2 simplifies to 1/16.
To apply the Product Rule of Exponents, you need to remember that when multiplying two numbers with the same base but different exponents, you add the exponents.
Let's break it down step by step:
First, simplify each component:
(1/2) to the power of 2 (2) = (1/2) ^ 2 = 1/4
(1/2) to the power of 2 (2) = (1/2) ^ 2 = 1/4
Now, multiply the simplified components together:
(1/4) * (1/4) = 1/16
Thus, (1/2) to the power of 2 (2) * (1/2) to the power of 2 (2) = 1/16.
Therefore, the final answer, in exponential simplest form, is (1/2) to the power of 2(2) = 1/16.