Final answer:
Exponents indicate repeated multiplication of a base number. To operate with exponents, you multiply the exponents when raising a power, add them when multiplying with a similar base, and subtract when dividing with a similar base.
Step-by-step explanation:
The exponent signifies how many times a number, known as the base, is multiplied by itself. When dealing with exponents, there are specific rules to follow when raising a power to another power, multiplying exponentiated numbers, or dealing with division (inverting) of exponentiated numbers. Let's consider these scenarios with examples:
Raising a Power to Another Power
When raising an exponentiated number to another power, you multiply the exponents. For example, (23)2 = 23×2 = 26.
Multiplying Exponentiated Numbers
For multiplication, if the base is the same, you add the exponents. For instance, 103 × 102 = 103+2 = 105.
Division of Exponentiated Numbers
When dealing with division, you subtract the exponent of the denominator from the exponent of the numerator if they have the same base, such as 103 / 101 = 103-1 = 102.