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:

${( {2}^{3} )}^{5} = {2}^{3 \times 5 } = {2}^{15}$