How to Solve Negative Exponents: A Simple Guide

Understanding Negative Exponents

• 💡 A negative exponent indicates that a base number should be moved to the opposite side of a fraction bar, changing the sign of the exponent.
• ⚡ For example, to solve 2 raised to the -3 (2⁻³), you can rewrite it as 1 divided by 2 raised to the positive 3 (1/2³).

Converting Negative to Positive Exponents

• 🔑 The core rule is that moving a base with an exponent across the fraction bar inverts the base and changes the exponent's sign.
• 🚀 If you have a number like 4⁻², moving the 4 to the denominator changes it to 1/4².

Evaluating Expressions with Negative Exponents

• 🧠 To evaluate 1/2³, you calculate 2 * 2 * 2, which equals 8. Therefore, 2⁻³ is 1/8.
• 📊 For 4⁻², you first get 1/4², and then calculate 4 * 4, which is 16. So, 4⁻² equals 1/16.

Additional Examples

• 🎯 Solving 3⁻³ involves rewriting it as 1/3³, and since 3 * 3 * 3 equals 27, the answer is 1/27.
• ✅ Similarly, 5⁻² is converted to 1/5², and 5 * 5 equals 25, making the final answer 1/25.