Explain the difference between multiplication and exponents by showing that 4 x 3 means adding four three times, and 4^3 equals 4 x 4 x 4. Reinforce the concept with this simple activity. Gather a large pile of blocks. State that you are going to multiply four by three. Ask for three volunteers and give each child four blocks. Ask the class to count the total number of blocks. They will reply that there are 12 blocks. Now ask for the answer to 4^3. Ask for four volunteers and give them four blocks each. The total is 16 blocks. Tell the class that they now have to multiply the 16 by 4 because four has to be multiplied by itself three times. Now you need four volunteers. Give each child 16 blocks. Ask the class to total the number of blocks. They may be astonished at the result
An operation with a radical is the opposite of an exponent operation. If 4^2 is 16, then the square root of 16 is 4. Use the blocks to demonstrate 4^2. Take four sets of four blocks. Have the students add them. There are 16 blocks. Now explain that to find the root of 16 you have to reverse the operation. The root is the number by itself. So remove three sets of four blocks. You will be left with four blocks.
Create a worksheet by dividing a sheet of paper into two columns. On one side write exponent problems, and on the other side write problems with radicals, to demonstrate how one activity is the opposite of the other. For example:
Solve the following problems: 4^3 (cube root of 64), 3^2 (square root of 9), 5^3 (cube root of 125) and 3^4 (fourth root of 81).
You can add problems appropriate to your student's skill level.
Provide the students with graph paper. Ask them to solve the following problems and then color in the appropriate number of squares: 3 x 3, 3^3, 4 x 4, 4^4, 5 x 5 and 5^5. This provides a visual demonstration of the difference between multiplication and exponents. You can add more problems to solve.