Exploring Zero to the Zero Power

Use the f(x)=a^x checkbox to show the function and move slider "a" to explore different bases for the function. Use the Sequence b(x) checkbox to reveal the sequence for b(x)= b^x. Move the slider "b" to explore the sequence values for the function. To explore the same function and sequence click the "set a=b". To explore the exact values of the sequence, click the "Show sequence point values" checkbox.
1. What do you notice when you set the function f(x)=a^x so that a=0? 2. What do you notice when you set the sequence b^x so that b=0? 3. What do the observations above tell us about when we raise zero to the zero power? Using this applet explore reasons for your answer to question 3. (Hint: you can use the sequence value patterns, exponential function rules, and observations of limits)