Evaluate $y =\left(\frac{1}{5}\right)^{ X }$ When $x = 0$.A. $y = 1$ B. $y = 0$ C. $y = \frac{1}{5}$

**Evaluating Exponential Functions: A Step-by-Step Guide** ===========================================================

Introduction

Exponential functions are a fundamental concept in mathematics, and understanding how to evaluate them is crucial for solving various mathematical problems. In this article, we will focus on evaluating the exponential function $y = \left(\frac{1}{5}\right)^{x}$ when $x = 0$. We will break down the problem step by step and provide a clear explanation of the solution.

What is an Exponential Function?

An exponential function is a mathematical function of the form $y = a^{x}$, where $a$ is a positive real number and $x$ is the variable. The function $y = a^{x}$ represents a curve that grows or decays exponentially as $x$ increases or decreases.

Evaluating $y = \left(\frac{1}{5}\right)^{x}$ when $x = 0$

To evaluate the function $y = \left(\frac{1}{5}\right)^{x}$ when $x = 0$, we need to substitute $x = 0$ into the function.

Step 1: Substitute $x = 0$ into the function

$y = \left(\frac{1}{5}\right)^{0}$

Step 2: Simplify the expression

When $x = 0$, any non-zero number raised to the power of 0 is equal to 1. Therefore, we can simplify the expression as follows:

$y = 1$

Conclusion

In conclusion, when $x = 0$, the value of the function $y = \left(\frac{1}{5}\right)^{x}$ is equal to 1.

Frequently Asked Questions

Q: What is the value of $y = \left(\frac{1}{5}\right)^{x}$ when $x = 1$?

A: To evaluate the function when $x = 1$, we need to substitute $x = 1$ into the function. This gives us:

$y = \left(\frac{1}{5}\right)^{1} = \frac{1}{5}$

Q: What is the value of $y = \left(\frac{1}{5}\right)^{x}$ when $x = -1$?

A: To evaluate the function when $x = -1$, we need to substitute $x = -1$ into the function. This gives us:

$y = \left(\frac{1}{5}\right)^{-1} = 5$

Q: What is the value of $y = \left(\frac{1}{5}\right)^{x}$ when $x = -2$?

A: To evaluate the function when $x = -2$, we need to substitute $x = -2$ into the function. This gives us:

$y = \left(\frac{1}{5}\right)^{-2} = 25$

Q: What is the value of $y = \left(\frac{1}{5}\right)^{x}$ when $x = 2$?

A: To evaluate the function when $x = 2$, we need to substitute $x = 2$ into the function. This gives us:

$y = \left(\frac{1}{5}\right)^{2} = \frac{1}{25}$

Conclusion

In conclusion, we have evaluated the exponential function $y = \left(\frac{1}{5}\right)^{x}$ for various values of $x$. We have shown that the function grows or decays exponentially as $x$ increases or decreases.

Final Answer

The final answer is: $\boxed{1}$