Certainly! Let's solve the problem step-by-step.
1. If the base is 4, what is the value if the exponent is 2?
To find the value, we use the formula for exponents:
[tex]\[ \text{base}^{\text{exponent}} \][/tex]
So, for a base of 4 and an exponent of 2:
[tex]\[ 4^2 = 4 \times 4 = 16 \][/tex]
Thus, when the exponent is 2, the value is [tex]\(16\)[/tex].
2. What is the value if the exponent is -2?
Negative exponents indicate that we should take the reciprocal of the base raised to the positive exponent. The formula for a negative exponent [tex]\(n\)[/tex] is:
[tex]\[ \text{base}^{-\text{exponent}} = \frac{1}{\text{base}^{\text{exponent}}} \][/tex]
So, for a base of 4 and an exponent of -2:
[tex]\[ 4^{-2} = \frac{1}{4^2} = \frac{1}{16} = 0.0625 \][/tex]
Thus, when the exponent is -2, the value is [tex]\(0.0625\)[/tex].
Summarizing the results:
- For an exponent of 2, the value is [tex]\(16\)[/tex].
- For an exponent of -2, the value is [tex]\(0.0625\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{16, \frac{1}{16}} \][/tex]
