Exponents are used to represent repeated multiplication of a number, called the base. An exponent tells how many times the base is multiplied by itself. For example, in 53, the base is 5 and the exponent is 3, meaning 5 multiplied by itself 3 times, or 5 x 5 x 5 = 125. Common mistakes involve treating exponents like regular multiplication, such as writing 4 x 3 = 12 instead of recognizing 4^3 means 4 x 4 x 4 = 64. Practice problems are provided to help students learn to identify the base and exponent in expressions and calculate their values.