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the multiple means the number used to multiply. And the factor means a number to multiply or divide by
The number 1.
The rule is that you multiply the exponents. So if I have 2 squared and I want to raise it to the third power, you multiply the 2x3=6. When you multiply powers you add the exponents. When you raise exponents to a power you multiply. This works for rational exponents which can be used to represent roots as well.
Multiplicand times multiplier equals product
The are used to represent numbers using powers of ten.