IM 8.7.8 Lesson: Combining Bases
Evaluate
Evaluate
The table contains products of expressions with different bases and the same exponent. Complete the table to see how we can rewrite them. Use the “expanded” column to work out how to combine the factors into a new base.
Can you write with a single exponent?
What happens if neither the exponents nor the bases are the same? Explain or show your reasoning.
There is an applet below for creating a visual display to play a game. Divide the display into 3 columns, with these headers:
How to play:
When the time starts, you and your group will write as many expressions as you can that equal a specific number using one of the exponent rules on your board. When the time is up, compare your expressions with another group to see how many points you earn.
How many points did you earn?
You have probably noticed that when you square an odd number, you get another odd number, and when you square an even number, you get another even number. Here is a way to expand the concept of odd and even for the number 3. Every integer is either divisible by 3, one more than a multiple of 3, or one less than a multiple of 3. Examples of numbers that are one more than a multiple of 3 are 4, 7, and 25. Give three more examples.
Examples of numbers that are one less than a multiple of 3 are 2, 5, and 32. Give three more examples.
Do you think it’s true that when you square a number that is a multiple of 3, your answer will still be a multiple of 3?
How about for the other two categories? Try squaring some numbers to check your guesses.