College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Evaluate [tex]$5^x$[/tex] if [tex]$x = -5$[/tex].

A. [tex]$\frac{1}{3125}$[/tex]
B. -25
C. -3125
D. [tex]$-\frac{1}{3125}$[/tex]

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].