How to Calculate Negative Exponents on Ti-84 Plus Calculator

Introduction

Negative exponents might seem confusing at first, but they follow a simple rule: a negative exponent indicates the reciprocal of the base raised to the positive exponent. For example, \( x^{-n} = \frac{1}{x^n} \).

The TI-84 Plus calculator can handle negative exponents easily, but you need to know the correct syntax to enter them properly. This guide will show you exactly how to do it.

Negative Exponents Basics

Before diving into the calculator, let's understand what negative exponents mean. A negative exponent indicates how many times to divide one by the base. For example:

This means that \( 2^{-3} \) is equal to one divided by 2 cubed, which equals 1/8.

Key Points About Negative Exponents

• Negative exponents represent reciprocals of positive exponents.
• The base remains the same; only the exponent changes.
• Negative exponents can be used with any real number except zero.

Calculating Negative Exponents on TI-84 Plus

Now that you understand the concept, let's see how to calculate negative exponents on your TI-84 Plus calculator.

Step-by-Step Instructions

1. Turn on your TI-84 Plus calculator and press the [MODE] key to ensure it's in the correct mode.
2. Press the [2ND] key and then the [CATALOG] key to open the catalog.
3. Scroll down to find the "A to the B" function (it's listed as "A^B").
4. Press [ENTER] to select the "A^B" function.
5. Enter the base number (the number you want to raise to a power).
6. Press the [COMMA] key to separate the base from the exponent.
7. Enter the negative exponent (e.g., -3).
8. Press [ENTER] to calculate the result.

Example Calculations

Let's look at a few examples to solidify your understanding.

Example 1: Simple Negative Exponent

Calculate \( 5^{-2} \):

1. Press [2ND] [CATALOG] to open the catalog.
2. Scroll to and select "A^B".
3. Enter 5, press [COMMA], then enter -2.
4. Press [ENTER]. The result should be 0.04 (which is \( \frac{1}{25} \)).

Example 2: Negative Exponent with a Fraction

Calculate \( \left(\frac{1}{2}\right)^{-3} \):

1. Press [MATH] and select "A/B" to enter a fraction.
2. Enter 1 in the numerator and 2 in the denominator.
3. Press [2ND] [CATALOG] to open the catalog.
4. Scroll to and select "A^B".
5. Enter the fraction, press [COMMA], then enter -3.
6. Press [ENTER]. The result should be 8 (which is \( 2^3 \)).

Common Mistakes

Even with the right steps, it's easy to make mistakes. Here are some common pitfalls to avoid:

• Forgetting to press the [COMMA] key between the base and exponent. This will cause an error.
• Entering a negative sign before the base instead of the exponent. For example, entering -5^-2 instead of 5^-2 will give a different result.
• Not using the correct function for exponents. Make sure you're using "A^B" and not another function.