Evaluate negative exponents

Key Notes :

🌟 Evaluate Negative Exponents 🌟

🔹 What Are Exponents?

An exponent shows how many times a number (called the base) is multiplied by itself.

• 👉 Example: 2³=2×2×2=8

🔹 What Are Negative Exponents?

A negative exponent means take the reciprocal (flip the base) and make the exponent positive.

👉 Example:

• 2⁻³=1/2³=1/8

🧠 Rule:

a⁻ⁿ=1/aⁿ (where a≠0)

🔹 Examples

1. 5⁻²=1/5²=1/25
2. 10⁻¹=1/10¹=1/10
3. (2/3)⁻²=(3/2)²=9/4​

🔹 Important Properties of Exponents

1. Product of powers:

a^m×aⁿ=a^m+n

2. Quotient of powers:

a^m/aⁿ=a^m−n

3. Power of a power:

(a^m)ⁿ=a^m×n

4. Zero exponent:

a⁰=1 (where a≠0)

5. Negative exponent:

a⁻ⁿ=1/aⁿ

🔹 Real-Life Application 🌍

Negative exponents are used in:

• Scientific notation for small numbers:
  2.5×10⁻³=0.0025
• Physics and Chemistry to represent very small quantities like charge, mass, or wavelength.

🔹 Quick Tip 💡

Always remember:

• Negative exponents don’t make the value negative,
• they just flip the fraction!

🧩 Practice Problems

1. 3⁻²=?
2. 1/4⁻³=?
3. (5²)⁻¹=?
4. 2⁻⁴×2³=?
5. (1/2)⁻²=?

Learn with an example

Let’s practice!🖊️