Radicals and Exponents

Exponents and Radicals

Extra work for teaching the teacher

By Owen Reynolds

Exponents are numbers, such as 5, 3 ½, or -20 that have small numbers next to them. An example is 2³. The big number is called the base, and the small number is called the exponent.

Exponents

​Radicals are also numbers, but they have a special symbol surrounding the number. It looks like this:

√

There is a number to the right of this symbol. Sometimes there is a line above the number, connecting to the symbol. There can also be a small number (or big number) to the left of the symbol. That depicts the type of radical.

​Radicals

Exponents

Further Explanation

The exponent depicts the number of times you multiply by the base. So if the exponent is four and the base is three, you multiply by three, four times. The equation would be:

3x3x3x3

If the exponent is composite, you can simplify like fractions and multiply by the base by the factor, and divide the exponent by the factor. So, an example is 3⁴ or 9². The way to say exponents is "[base] to the [exponent] power". But with 2 being the exponent, you could say "[base] squared" and with the exponent being 3, you could say "[base] cubed". If the exponent is a fraction, you first find the numerator and power the base. Then you find the denominator and use that as a radical (further explained later). When you multiply exponents and the base is the same, you add the exponents and keep the base the same. But if you multiply and the power is the same, then you multiply the bases. You can do either but not both if they are the exact same. The same is for dividing but you subtract the exponents. If you do a power to a power, you multiply the powers.

Multiple Choice

What is 2³?

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