Question

One of your friends sends you an email asking you to explain how all of the following expressions have the same answer.
the cube root of x cubed

:x to the one–third power • :x to the one–third power • x to the one–third power

1 over x to the –1 power

the eleventh root of the quantity of x to the fifth times x to the fourth times x squared

Answer 1

∛x³ = x^(3/3) = x^1 = x

x^(1/3 + 1/3 + 1/3) = x^(3/3) = x

1/x^-1 = x^1 = x

¹¹√(x^(5+4+2) = ¹¹√x^11
= x^(11/11) = x^1
= x