Exponents and radicals are a core skill when it comes to transitioning to algebra, and many students struggle with the way that the concepts are presented in texts. Some have a hard time differentiating between exponents and multiplication as well as radicals and division.
Understanding Exponents
Using visual aids such as marbles is a great way to wrap your head around the idea of exponents. If you have two marbles in a group and there are three groups, then there are six marbles all together. This is like saying 3 groups of 2 makes 6, a multiplication problem. If you think, ___ x___ , the numbers represent what goes in the blanks. Exponents are a special type of multiplication where the exponent represents how many blanks there are instead of what goes in them. The base is the big number and the exponent, or power, is the small number. If you have 2 to the fourth power, that means you have four blanks: ___ x ____ x ____ x ____. The base goes in every blank, so 2 to the fourth power is 2 x 2 x 2 x 2. To represent this with marbles, think two groups with two groups in each with two groups in each of those and with two marbles in each of the last groups. Draw circles for the groups: two big ones with two smaller ones in each, two tiny ones in each of those, and two marbles in each tiny circle. Notice that numbers get bigger much faster with exponents than with multiplication.
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