Answer :
Certainly! Let's evaluate [tex]\(5^x\)[/tex] when [tex]\(x = -5\)[/tex].
1. Understand the expression: We need to find the value of [tex]\(5^{-5}\)[/tex].
2. Use the property of exponents: A negative exponent means we take the reciprocal of the base raised to the positive of that exponent. This means:
[tex]\[
5^{-5} = \frac{1}{5^5}
\][/tex]
3. Calculate [tex]\(5^5\)[/tex]:
- First, compute powers step by step:
[tex]\[
5^1 = 5
\][/tex]
[tex]\[
5^2 = 5 \times 5 = 25
\][/tex]
[tex]\[
5^3 = 5 \times 25 = 125
\][/tex]
[tex]\[
5^4 = 5 \times 125 = 625
\][/tex]
[tex]\[
5^5 = 5 \times 625 = 3125
\][/tex]
4. Find the reciprocal:
[tex]\[
5^{-5} = \frac{1}{3125}
\][/tex]
5. Compare with the answer choices: Given the choices:
- (A) [tex]\(\frac{1}{3125}\)[/tex]
- (B) -25
- (C) -3125
- (D) [tex]\(-\frac{1}{3125}\)[/tex]
The correct answer is (A) [tex]\(\frac{1}{3125}\)[/tex].
And that's how you evaluate [tex]\(5^x\)[/tex] for [tex]\(x = -5\)[/tex].
1. Understand the expression: We need to find the value of [tex]\(5^{-5}\)[/tex].
2. Use the property of exponents: A negative exponent means we take the reciprocal of the base raised to the positive of that exponent. This means:
[tex]\[
5^{-5} = \frac{1}{5^5}
\][/tex]
3. Calculate [tex]\(5^5\)[/tex]:
- First, compute powers step by step:
[tex]\[
5^1 = 5
\][/tex]
[tex]\[
5^2 = 5 \times 5 = 25
\][/tex]
[tex]\[
5^3 = 5 \times 25 = 125
\][/tex]
[tex]\[
5^4 = 5 \times 125 = 625
\][/tex]
[tex]\[
5^5 = 5 \times 625 = 3125
\][/tex]
4. Find the reciprocal:
[tex]\[
5^{-5} = \frac{1}{3125}
\][/tex]
5. Compare with the answer choices: Given the choices:
- (A) [tex]\(\frac{1}{3125}\)[/tex]
- (B) -25
- (C) -3125
- (D) [tex]\(-\frac{1}{3125}\)[/tex]
The correct answer is (A) [tex]\(\frac{1}{3125}\)[/tex].
And that's how you evaluate [tex]\(5^x\)[/tex] for [tex]\(x = -5\)[/tex].
