Which of the following is equal to x^(3/2)?

Hi onyx12102,

You must know the following basic rules of exponents and roots:-
1) Fraction as a power:-
\(a^{\frac{1}{n}}=\sqrt[n]{a}\) and vice-versa
2) Keep the base, add the exponent (add for multiplication)
\(a^n*a^m=a^{n+m}\) and vice-versa

So, \(x^{1+\frac{1}{2}}\) can be written as \(x^1*x^{\frac{1}{2}}\) (Using rule(2) above, n=1, m=\(\frac{1}{2}\), a=x)

Now, \(x^{\frac{1}{2}}\) can be written as (\(\sqrt{x}\) Using rule(1) above,a=x, n=2 )

Hence, \(x^1*x^{\frac{1}{2}}\) =\(x*\sqrt{x}\)

Hope it helps.

Note:- \(\sqrt[n]{a}=\sqrt{a}\) . The symbol '√' unless specified, it refers to square root operation. So no need to mention 2 on the lap of √. By default '√' means a square root operation.


P.S:- You may visit https://gmatclub.com/forum/exponents-an ... 74993.html master thread for more tips on exponents and roots.

PKN Thank you

I eventually worked it out but I think it's beneficial to other beginners to see how you got there. Thanks alot

The underlying rule that's being tested here is how you can convert fractional exponents into roots:

--> x^3/2.

Remember that: the numerator is the power of the base, the denominator is the root. When we convert it into its root we get:

--> √x^3

This is the same as:

--> √x*x*x.

If we take the square of all the variables, we are left with:

--> x√x

wouldn't the method you used only be true if we know x > 0?