Evaluating Powers with Negative Exponents

Exponents help us understand how numbers grow or shrink. But what happens when the exponent is negative?

Let’s explore! 

What Are Exponents?

An exponent tells us how many times to multiply a number by itself.

Example:

But what about negative exponents? Do they mean we multiply by negative numbers? Not quite!

Understanding Negative Exponents

A negative exponent means we take the reciprocal (flip the fraction) of the base.

Rule:

 Examples:

Why Do Negative Exponents Work Like This?

Think about this pattern:

 Notice how each step divides by 2? That’s why negative exponents flip the base into a fraction!

Common Mistakes to Avoid

❌ Thinking negative exponents make the base negative

❌ Forgetting to apply the exponent first

Real-Life Applications of Negative Exponents

 Science & Medicine

Microorganisms are tiny, and their sizes are often written using negative exponents.

 Example:  

Physics & Engineering

Negative exponents help describe small values, like wavelengths of light or nanotechnology.

Example: A red light wavelength is around meters.

 Finance & Economics

Interest rates and depreciation use negative exponents to model exponential decay.

Example: A car’s value decreases by per year.

Mastering negative exponents helps us understand the tiny details of the world!

Let’s explore more and practice with the help of Designed Worksheets at NumericWiz!