SOLUTION: DEFINITIONS AND RULES FOR EXPONENTS.:Explain three rules for exponents Product Rule: Quotient Rule: Power Rule: Raising a product to a power: Raising a quotient to a power:

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Question 405545: DEFINITIONS AND RULES FOR EXPONENTS.:Explain three rules for exponents
Product Rule:
Quotient Rule:
Power Rule:
Raising a product to a power:
Raising a quotient to a power:
Scientific notation:

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Rule 1.
Same Base...=>...
a%5Em%2Aa%5En+=+a%5E%28m+%2B+n%29.....To multiply powers of the same base, add the exponents.

Rule 2:
Power of a Product of Factors
%28ab%29%5En+=+a%5Enb%5En.........

Rule 3:
Power of a Power
%28a%5Em%29%5En+=+a%5Emn...........to take a power of a power, we multiply the exponents



Raising a product to a power:
When a product is raised to a power, we can distribute that power through to each term in the product. That is
%28ab%29%5En+=+a%5Enb%5En
This is true for all kinds of exponents, positive and negative (and as we will see later, fractional).

Raising a quotient to a power:


Raising a quotient to a power can be done by using the formula for raising products to a power:

In general, this means that we can distribute the power over each term in the quotient:
%28a%2Fb%29%5En=+a%5En%2Fb%5En
Scientific notation:
To make writing and dealing with these very+large and very+small numbers easier, scientists developed scientific notation.
Fraction Decimal Exponential Notation
1%2F1000 0.001+ 10%5E-3
Every non-zero number can be written in scientific notation. For example,
100=1%2A10%5E2
4321=4.321%2A10%5E3
0.0007925=7.925%2A10%5E-4 and so on