The exponent of a number says how many times to use the number in a multiplication.
You are watching: -3 to the power of 2
In 82 the “2” says to use 8 twice in a multiplication,so 82 = 8 × 8 = 64
In words: 82 could be called “8 to the power 2” or “8 to the second power”, or simply “8 squared”
Exponents are also called Powers or Indices.
Some more examples:
Example: 53 = 5 × 5 × 5 = 125
In words: 53 could be called “5 to the third power”, “5 to the power 3” or simply “5 cubed”
Example: 24 = 2 × 2 × 2 × 2 = 16
In words: 24 could be called “2 to the fourth power” or “2 to the power 4” or simply “2 to the 4th”
So in general:
an tells you to multiply a by itself,so there are n of those a“s: |
Another Way of Writing It
Sometimes people use the ^ symbol (above the 6 on your keyboard), as it is easy to type.
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Negative Exponents
Negative? What could be the opposite of multiplying? Dividing!
So we divide by the number each time, which is the same as multiplying by 1number
Negative? Flip the Positive!
That last example showed an easier way to handle negative exponents: Calculate the positive exponent (an) |
More Examples:
Negative Exponent Reciprocal ofPositive Exponent Answer4-2 | = | 1 / 42 | = | 1/16 = 0.0625 |
10-3 | = | 1 / 103 | = | 1/1,000 = 0.001 |
(-2)-3 | = | 1 / (-2)3 | = | 1/(-8) = -0.125 |
What if the Exponent is 1, or 0?
1 | If the exponent is 1, then you just have the number itself (example 91 = 9) | |
0 | If the exponent is 0, then you get 1 (example 90 = 1) | |
But what about 00 ? It could be either 1 or 0, and so people say it is “indeterminate”. |
It All Makes Sense
If you look at that table, you will see that positive, zero ornegative exponents are really part of the same (fairly simple) pattern:
Example: Powers of 5.. etc..
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52 | 5 × 5 | 25 | |
51 | 5 | 5 | |
50 | 1 | 1 | |
5-1 | 15 | 0.2 | |
5-2 | 15 × 15 | 0.04 | |
.. etc.. |