Understanding negative exponents
A negative exponent doesn't make a number negative! Instead, it means 'reciprocal' or 'flip'. It's a way of writing very small numbers (fractions) using the power of exponents.
Concept
A negative exponent is a way of writing a fraction without the fraction bar. It indicates the reciprocal of the base raised to the positive exponent. **The Rule of Negative Exponents:** **x⁻ⁿ = 1/xⁿ** In simple terms, a negative exponent tells you to move the base to the other side of the fraction line and make the exponent positive. **Visualizing the Pattern:** Let's look at the powers of 2: * 2⁴ = 16 * 2³ = 8 (divide by 2) * 2² = 4 (divide by 2) * 2¹ = 2 (divide by 2) * 2⁰ = 1 (divide by 2) * 2⁻¹ = 1/2 (divide by 2) * 2⁻² = 1/4 (divide by 2) * 2⁻³ = 1/8 (divide by 2) As you can see, the pattern of dividing by the base continues into the negative exponents, creating fractions. **Examples:** * **5⁻²** = 1 / 5² = **1/25** * **10⁻³** = 1 / 10³ = **1/1000** = **0.001** * **(1/3)⁻²** = 1 / (1/3)² = 1 / (1/9) = **9** (Flipping a fraction moves the denominator to the top!) **What about a negative exponent in the denominator?** The same rule applies, but in reverse. It moves to the numerator. **1 / x⁻ⁿ = xⁿ** * **1 / 3⁻²** = 3² = **9** **Key Idea:** A negative exponent is an instruction to "flip" the location of the base. If it's in the numerator, move it to the denominator. If it's in the denominator, move it to the numerator. Then, make the exponent positive.
Try it
Practice: Understanding negative exponents.