Complete the following statement. As the value of n in the expression (1/4)^n increases, the value of the expression is?
I need help with this question.
(1/4)^2 = (1/4)(1/4) = 1/16
(1/4)^3 = (1/4)(1/4)(1/4) = 1/64
etc
The sentence says to complete it not answer it.
Can you explain to me how you got the answer?
To complete the statement, we need to analyze how the value of the expression changes as the value of n increases in the expression (1/4)^n.
The expression (1/4)^n represents raising the fraction 1/4 to the power of n.
When you raise a fraction to a power, you are essentially multiplying the fraction by itself multiple times.
Let's start by evaluating some values of the expression for different values of n:
For n = 0: (1/4)^0 = 1
For n = 1: (1/4)^1 = 1/4
For n = 2: (1/4)^2 = 1/16
For n = 3: (1/4)^3 = 1/64
From these calculations, we observe that as the value of n increases, the value of the expression (1/4)^n decreases.
In other words, as n gets larger, the fraction 1/4 is being divided by itself more times, resulting in a smaller value.
To summarize, as the value of n in the expression (1/4)^n increases, the value of the expression decreases.