Question

guided practice
exponential functions
type your answer and then click or tap done.
what is the value of 0.5(0.5)^0?

x	0.5(0.5)^x	y
-2	0.5(0.5)^{-2}	0.2
-1	0.5(0.5)^{-1}	1
0	0.5(0.5)^0
1	0.5(0.5)^1
2	0.5(0.5)^2	0.125

Explanation:

Step1: Recall the zero - exponent rule

The zero - exponent rule states that for any non - zero real number \(a\), \(a^{0}=1\). In the expression \(0.5(0.5)^{0}\), the base \(a = 0.5\) which is non - zero. So, \((0.5)^{0}=1\).

Step2: Multiply the remaining terms

Now we have the expression \(0.5\times(0.5)^{0}=0.5\times1\) (since we found that \((0.5)^{0} = 1\) from Step 1). When we multiply \(0.5\) by \(1\), we get \(0.5\times1 = 0.5\).

Answer:

0.5