Question

9 - Who is correct?Maria stated this: If x3=729then x313=72913Jordan stated this: If x3=729 then x=3729

Answer 1

Both maria and jordan are correct

Answer 2

Step-by-step explanation

First of all, it's important to remember the relation between radicals and exponents:

`\sqrt[n]{x}=x^{(1)/(n)}`

So if we have the following equation:

`x^3=729`

We can solve it in two ways. On the one hand we can apply a cubic root at both sides:

`\begin{gathered} \sqrt[3]{x^3}=\sqrt[3]{729} \\ x=\sqrt[3]{729} \end{gathered}`

On the other hand, we can raised both sides to 1/3 which is the same as applying a cubic root:

`\begin{gathered} (x^3)^{(1)/(3)}=729^{(1)/(3)} \\ x=729^{(1)/(3)} \end{gathered}`Answer

As we saw, both Maria and Jordan are correct, they just used different notations.