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Special Cases

The zero exponent

Each one of these problems is solved by using a 1 multiplied by the number, the amount of times the exponent indicates. If the exponent is 0, the 1 isn't multiplied by the number at all. Therefore, the answer is 1. This is an important rule to remember. It will be explained better in the next page of this lesson.

510
1

Zero with an exponent:

In most cases zero with an exponent can be calculated like any other number and exponent.

04
1 * 0 * 0 * 0 * 0
0

Note that as long as 1 is being multiplied by at least one 0, the end result is 0. Therefore we can conclude that 0 to any positive exponent is always zero.

Another special case occurs with 00. Zero with an exponent of zero is undefined, and cannot be calculated.

Be careful not to the rules for zero exponents! Zero to any positive power is always zero, because no matter how many times you multiply the 1 by zero the answer will always be zero. But 00 is undefined.

The 1 exponent:

Consider this example in which rasies a number is raised to the first power.

511
1 * 51
51

If you try any similar example such as 101 or 1001, you will find that the result is always the original number or base. This is because 1 times any other number is always equal to the second number.

So to simplify the case where a number is raised to the first power, we can simply remove the exponent.

The next page presents another special case and explains how to read exponents.


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