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What are Exponents?

Exponents are sometimes referred to as powers and means the number of times the 'base' is being multiplied. In the study of algebra, exponents are used frequently. In the example to the right, one would say: Four to the power of 2 or four raised to the second power or four to the second. This would mean 4 x 4 or (4) (4) or 4 · 4 . Simplified the example would be 16.

If the power/exponent of a number is 1, the number will always equal itself. In other words, in our example if the exponent 2 was a 1, simplified the example would then be 4.

Exponent Rules

When working with exponents there are certain rules you'll need to remember.

When you are multiplying terms with the same base you can add the exponents.

This means: 4 x 4 x 4 x 4 x 4 x 4 x 4 or 4 · 4 · 4 · 4 · 4 · 4 · 4

When you are dividing terms with the same base you can subtract the exponents.

This means: 4 x 4 x 4 or 4 · 4 · 4

When parenthesis are involved - you multiply. (83)2 =86

yayb = y (a+b)

yaxa = (yx)a

Squared and Cubed and 0's
When you multiply a number by itself it is referred to as being 'squared'. 42 is the same as saying "4 squared" which is equal to 16.
If you multiply 4 x 4 x 4 which is 43 it is called 4 cubed. Squaring is raising to the second power, cubing is raising to the third power. Raising something to a 1 means nothing at all, the base term remains the same. Now for the part that doesn't seem logical. When you raise a base to the power of 0, it equals 1. Any number raised to the power 0 equals 1 and 0 raised to any exponent or power is 0!

Deb Russell