[size=150]Evaluate [/size][math]5^{^3}\cdot2^{^3}[/math]

[size=150]Evaluate [math]10^{^3}[/math][/size]

Can you write [math]2^3\cdot3^{^4}[/math] with a single exponent?

What happens if neither the exponents nor the bases are the same? Explain or show your reasoning.

[br][table][tr][td][math]a^n\cdot a^m=a^{n+m}[/math][/td][td][math]\frac{a^n}{a^m}=a^{n-m}[/math][/td][td][math]a^n\cdot b^n=(a\cdot b)^n[/math][/td][/tr][/table][br]How to play:[br][br]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.[br][br][list][*]Your group gets 1 point for every [i]unique[/i] expression you write that is equal to the number and follows the exponent rule you claimed.[/*][*]If an expression uses negative exponents, you get 2 points instead of just 1.[/*][*]You can challenge the other group’s expression if you think it is not equal to the number or if it does not follow one of the three exponent rules.[/*][/list][br]How many points did you earn?[br]

[size=150]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 [i]more[/i] than a multiple of 3, or one [i]less[/i] than a multiple of 3.[br][/size][br]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.