Explain the rules of exponents and provide one example of each:

Multiplying Monomials:
Product of Powers
Power of Power
Power of a Product

Dividing Monomials:
Quotient of Powers
Power of a Quotient

Please help.

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The rules of exponents are:

a^n a^m = a^{n+m}
If you multiply two powers of the same element, the result is the same as rasing this element to the power that is the sum of n and m.
For natural n and m this result can be explained as follows:

a^n is a multiplied by itself a times. So, we have a^n=(a a a ... a) with precisely n factors.
a^m is a multiplied by itself m times. So we have a^m=(a a a ... a) with precisely m factors.
Now, look at the product (a^n)(a^m). Expanding a^n and a^m as above we get:
(a^n)(a^m) = (a a...a)(a a...a), with n factors of a in the first set of parentheses, and m factors of a in the second set of parentheses. But together they form the product of a ...

Solution Summary

The Laws of exponents are explained and illustrated with examples

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Please explain how you came up withthe answers when completed. Thanks.
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