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Law of Exponents
The exponents of a number is when how many times to use the number in multiplication.
8^3 = 8 X 8 X 8 = 512
In other words, 8^3 could be called “8 to the third power”, “8 to the power of 3”, or simply “8 cubed”
8 is the base while 3 is the exponent or index
Another example: 3^4 = 3 X 3 X 3 X 3 = 81
So an exponents saves use writing out lots of multiplies!
For example: a ^7
a^7 = a x a x a x a x a x a x a = aaaaaaaa
For example: x^6 = xxxxxx
The Key to the Laws
Writing all the letters down is the key to understanding the Laws.
Example: x^2x^3 = (xx)(xxx) = xxxxx = x^5
The key to the law is just to remember to write down all the letters ( as many as the exponents tells you to) and see if you can make sense of it.
The “Laws of Exponents come from three ideas:
The exponent says how many times to use the number in multiplication
A negative exponent means divide because the opposite of multiplying is dividing
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