Question

Mike claims that (2^3)^5= 2^15. Sarah claims that (2^3)^5= 2^8. Who is correct? Explain your reasoning.

Answer 1

Mike is correct, because the rules for powers and exponentiation say that when you elevate a certain base which is already being elevated to a certain power, the powers multiply.

This means that:

`{( {a}^(b) )}^(c) = {a}^(bc)`

Or, using your example:

`{( {2}^(3) )}^(5) = {2}^(3 * 5 ) = {2}^(15)`