1. Clare said, “I know that , , and . I wonder what means?”

   First, she graphed for some whole number values of , and estimated from the graph.

   1. Graph the function yourself. What estimate do you get for ?

      

   2. Using the exponent rules, Clare evaluated . What did she get?
   3. For that to be true, what must the value of be?
2. Diego saw Clare’s work and said, “Now I’m wondering about .”

   First he graphed for some whole number values of , and estimated from the graph.

   1. Graph the function yourself. What estimate do you get for ?

      

   2. Next he used exponent rules to find the value of . What did he find?
   3. Then he said, “That looks like a root!” What do you think he means?

Use the exponent rules and your understanding of roots to find the exact value of:

Match each exponential expression to an equivalent expression.