Scientists Say: Exponent

Exponent (noun, “EX-poh-nent”)

An exponent is a number that tells you how many times to multiply a number by itself.

In math, an exponent appears as a superscript after another number:

2³ = x

In this equation, 3 is the exponent. The number 2 is called the base. The equation above asks, if I multiply 2 by itself 3 times, what number will I get?

2³ = 2 × 2 × 2 = x

In this case, solving for x gives us 8.

2³ = 2 × 2 × 2 = 8

This equation tells us to what power — or exponent — we must “raise” 2 to get our answer. Spoken out loud, we would say: Base 2 raised to the power of 3 equals 8.

Exponents can help simplify big or small numbers. This approach is called scientific notation. Scientists may use this format to express a huge number.

Consider the distance from Earth to the sun. That’s about 150,000,000 kilometers (93,000,000 miles). Instead of writing so many zeros, scientists may simplify this number using exponents. Then, 150,000,000 becomes 1.5 × 10⁸. This tells us that the first number —1.5 — must be multiplied by base 10 raised to the power of 8.

The approach works for really small numbers, too. Consider the width of a typical bacterium. That’s about 0.000001 meters (0.00004 inches). Scientists may simplify this number using a negative exponent. A negative exponent tells you how many times to divide by a number. Using this format, 0.000001 meters becomes 1 × 10^-6 meters.

Exponents also help scientists graph certain patterns of change. Exponential growth, for example, means that increases multiply upon themselves over time. (In contrast, some changes occur at a constant rate. That kind of change is described as linear.) Scientists may use an exponential scale to display bacterial growth in a petri dish. The spread of disease sometimes occurs on exponential scale, too.

In a sentence

Scientists use exponents to express huge numbers — such as values on a timeline spanning the life of the universe.

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