unit 2.4  Law of exponents:
Product of powers (Multiplication)
Quotient of powers (Division)
what we need to know
Powers: Bases and exponents (Definitions)
Powers with base of 10
Exponents of 0 and 1
Repeated multiplication
Powers with base of 10
Exponents of 0 and 1
Repeated multiplication
class Notes
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Remember that a product is a multiplication. The first law of exponents says that, to multiply powers with equal bases, the exponents must be added:
The second law of exponents, quotient of powers, allows us to divide powers of equal bases, Remember that "quotient" means division.
This law can be summarized as follows: When dividing powers of equal base, the exponents must be subtracted. This is the opposite of multiplication, and if you think about it, it makes sense: To multiply means to increase in number (addition), and to divide means to break up (subtraction).
This law can be summarized as follows: When dividing powers of equal base, the exponents must be subtracted. This is the opposite of multiplication, and if you think about it, it makes sense: To multiply means to increase in number (addition), and to divide means to break up (subtraction).
Here are some examples:
Take a look at the following example to understand why, when dividing, the exponents are subtracted. Remember that a number that's multiplying in the numerator of a fraction "cancels" the same number, which should also be multiplying, in the denominator of the same fraction:
To summarize:
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