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

\[\sqrt[3]{x^3} = x\]

\[x^{1/3} * x^{1/3} * x^{1/3} = x^{\frac{ 1 }{ 3 } + \frac{ 1 }{ 3 } + \frac{ 1 }{ 3 } } = x^{3/3} = x^1 = x\]

\[(\frac{ 1 }{ x })^{-1} = x^1 = x\]

\[\sqrt[11]{x^5 * x^4 * x^2} = \sqrt[11]{x^{5+4+2}} = \sqrt[11]{x^{11}} = x^{11/11} = x^1 = x \]

Understood why they are the same? :)

Answer 2

Yes, I can see now how they are related to each other when they are put like that.

Answer 3

Thank you for your help :)

Answer 4

:)