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Negative Exponents: Writing Powers of Fractions and Decimals

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  • 0:03 You Are Always You
  • 0:17 Exponents
  • 0:41 Negative Exponents
  • 1:24 It's Still the Same
  • 3:24 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe
Most numbers can be written in different ways, either as a fraction, decimal or exponent. This lesson will teach you how to write fractions and decimals using exponents and how to convert between the two.

You Are Always You

When you look back at pictures of yourself, do you ever stop and notice just how much you've changed? You might be skinnier, taller, have longer hair or even different color hair, but no matter how your appearance changes, you are still the same person. You are always you.

Exponents

An exponent is a superscript number whose purpose is to indicate how many times the main number (or base) should be multiplied to itself.

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In this example, the superscript '2' tells us to multiply the base '5' to itself two times, or 5 * 5, which is equal to 25.

Exponents can also be written with a carat, like this: 5^2.

Negative Exponents

Negative exponents are a bit different. They still indicate how many times to multiply a number to itself, but it also means that the base is on the wrong side of the fraction line, which means that if the negative exponent is in the numerator (top of a fraction), to make it positive, it needs to be switched to the denominator (bottom of a fraction).

3^-2 = 1 / 3^2

The reverse is also true. If the negative exponent is in the denominator, to make it positive, just move it to the numerator.

1 / 2^-5 = 2^5

It's Still the Same

Just like you are still the same person whether you have long hair or short hair, are fat or thin, the mathematical expression is the same regardless of whether it's written as a fraction, decimal or with a negative exponent.

So, 3^-3 can also be written as 1 / 3^3 or 1/27. It can also be written as a decimal. To write a fraction as a decimal, you just need to divide - in this case, divide 1 by 27 to get 0.037.

Let's try another one.

Write 4^-2 as a fraction and as a decimal.

First, to write it as a fraction, we know that the negative exponent will become positive when placed in the denominator of a fraction. So, we know that:

4^-2 = 1 / 4^2 = 1/16

Then, to write 1/16 as a decimal, simply divide.

1/16 = 0.0625

It even works with variables.

b^-5 = 1 / b^5

1 / y^-8 = y^8

Let's do one last example.

Write this term using only positive exponents. Simplify where possible.

(x^-8 * 3^3) / (4^-2 * y^2)

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