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Exponents

 

When you have finished this page, try the Exponents Quiz.

Exponents are a special form of multiplication in which a number is multiplied by itself. This is called raising a number to a power. Let's look at some examples.

In this example there is a three followed by a small two to the right and slightly above the three. The two written in this fashion is called superscript meaning super or above the other numbers or letters in a sentence. In math this means that the number before the number written in superscript is being raised to a certain power. In this example three is being raised to the second power, which means it is being multiplied by itself once or three times three which equals nine. Notice this is different than if one was multiplying three times two - this is why the second number is written in superscript so that there is less confusion.

This same equation can be written with a raised carat mark as in the second example. It means the same as the first example - that three is being raised to the second power.

3

2

= 9

 

3 ^ 2 = 9

Three to the third power would be three time three times three or twenty-seven.

Suppose you wish to add numbers with exponents - how is that done?

Two numbers with exponent or power can be added as in this example by converting the numbers with exponents to regular numbers.

2^2 + 3^2 = 13
4 + 9 = 13

However you cannot add the numbers together to get five to the second power as that is twenty-five.

2^2 + 3^2 = 13

5^2 = 25

You also cannot add the exponents together in an addition problem. Five to the fifth power equals five times five times five times five times five which equals three thousand one hundred twenty-five.

2^2 + 3^2 = 13

5^5 = 3125

Suppose you wish to multiply numbers with exponents. In this case one would multiply the numbers, but add the exponents. Let's look at an example.

2^2 * 2^3 = 32
4 * 8 = 32

 

Algebra Main Page Positive & Negative Numbers Addition & Subtraction of Positive & Negative Numbers Multiplication of Positive & Negative Numbers Division of Positive & Negative Numbers Order of Operations
Exponents Scientific Notation Equations 1 Equations 2 Equations 3

Equations 4

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