[math](\text{-}3)^2<3^2[/math]
[math](\text{-}3)^3=3^3[/math]
[math](\text{-}5)^2>\text{-}5^2[/math]
What patterns do you notice when you start with a fraction raised to a negative exponent and rewrite it using a single positive exponent? Show or explain your reasoning.
[size=150]Lin, Noah, Diego, and Elena decide to test each other’s knowledge of exponents with bases other than 10. They each chose an expression to start with and then came up with a new list of expressions; some of which are equivalent to the original and some of which are not.[br][br][/size][size=150]Choose the equivalent expressions.[br][/size][br]Lin’s original expression is [math]5^{-9}[/math] and her list is:
Noah’s original expression is [math]3^{10}[/math] and his list is:
Diego’s original expression is [math]x^4[/math] and his list is:[br]
Elena’s original expression is [math]8^0[/math] and her list is:
Choose 2 of the 4 lists to analyze. For each list of expressions you choose to analyze, explain your reasoning.