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

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Which of the following is equal to x^(3/2)? [#permalink]
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onyx12102 wrote:
PKN

x1+12x1+12
=x1∗x12=x1∗x12 =x∗x√=x∗x

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
$$a^n*a^m=a^{n+m}$$ 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.
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Re: Which of the following is equal to x^(3/2)? [#permalink]
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
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Re: Which of the following is equal to x^(3/2)? [#permalink]
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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
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Re: Which of the following is equal to x^(3/2)? [#permalink]
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Re: Which of the following is equal to x^(3/2)? [#permalink]
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