Simplify each expression.
4 to the 4th over 4 to the 6th
A. –16
B. 16
C. one sixteenth
D. –one sixteenth
well, that will be 4^4 / 4^6 = 4^-2 = 1/4^2 = ____
how about losing all the words and just writing the numbers?
To simplify the expression 4 to the 4th over 4 to the 6th, we can use the rule of exponents which states that when dividing two numbers with the same base, we subtract the exponents.
In this case, the base is 4. So, we subtract the exponent of 4 in the denominator (6) from the exponent of 4 in the numerator (4).
4 to the 4th can be written as 4 * 4 * 4 * 4, which equals 256.
4 to the 6th can be written as 4 * 4 * 4 * 4 * 4 * 4, which equals 4096.
Now, we can rewrite the expression as 256 over 4096.
To further simplify, we can divide both the numerator and the denominator by the greatest common factor, which in this case is 256.
256 divided by 256 equals 1, and 4096 divided by 256 equals 16.
Therefore, the simplified expression is 1 over 16, which can be written as 1/16 or one sixteenth.
So, the correct answer is C. one sixteenth.