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

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:

Or, using your example:

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.