Powers can be multiplied and divided. In the example below, we will use powers of 2 to form a rule about multiplying exponents. The table shows several powers of 2 and their values.
You can use
the table to substitute exponents for the factors of multiplication equations.
What do you notice about the exponents in the following products?
These
examples suggest that you can multiply powers with the same
base by adding the exponents. Think about a2 ⋅ a3.
Simplify
each expression.
1.
43 ⋅ 45
Alternative Solutions:
2.
x3 ⋅ x4
Alternative Solutions:
Alternative Solutions:
4.
(a3b2)(a2b4)
Alternative Solutions:
You can use
powers of 2 to help find a rule for dividing powers. Study each quotient in the
table. What do you notice about the exponents?
These
examples suggest that you can divide powers with the same base by subtracting
the exponents. Think about a5 ÷ a2.
Remember that you can write a division expression as a fraction.
Example
Simplify
each expression.
Alternative Solutions:
Alternative Solutions:
Alternative Solutions:
A special
case results when you divide a power by itself. Consider the following two ways
to simplify , where b ≠ 0.
Since cannot have two
different values, you can conclude that b0 = 1. Therefore,
any nonzero number raised to the zero power is equal to 1.
Example
Alternative Solutions:
Sumber
Thanks for reading Multiplying and Dividing Powers. Please share...!