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

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Math Expert
Joined: 02 Sep 2009
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Which of the following is equal to x^(3/2)?  [#permalink]

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26 Aug 2018, 20:11
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Difficulty:

15% (low)

Question Stats:

66% (00:42) correct 34% (00:39) wrong based on 155 sessions

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Which of the following is equal to $$x^{\frac{3}{2}}$$?

(A) $$x^2 \sqrt{x}$$

(B) $$x \sqrt{x}$$

(C) $$\sqrt[3]{x^2}$$

(D) $$\sqrt[3]{x}$$

(E) $$(x^3)^2$$

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WE: Supply Chain Management (Energy and Utilities)
Re: Which of the following is equal to x^(3/2)?  [#permalink]

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26 Aug 2018, 20:19
Bunuel wrote:
Which of the following is equal to $$x^{\frac{3}{2}}$$?

(A) $$x^2 \sqrt{x}$$

(B) $$x \sqrt{x}$$

(C) $$\sqrt[3]{x^2}$$

(D) $$\sqrt[3]{x}$$

(E) $$(x^3)^2$$

$$x^{\frac{3}{2}}$$ can be written as:

$$x^{1+\frac{1}{2}}$$
$$=x^1*x^{\frac{1}{2}}$$$$=x*\sqrt{x}$$

Ans. (B)
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Re: Which of the following is equal to x^(3/2)?  [#permalink]

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26 Aug 2018, 20:34
2
Bunuel wrote:
Which of the following is equal to $$x^{\frac{3}{2}}$$?

(A) $$x^2 \sqrt{x}$$

(B) $$x \sqrt{x}$$

(C) $$\sqrt[3]{x^2}$$

(D) $$\sqrt[3]{x}$$

(E) $$(x^3)^2$$

Below rules are used:
$$x^{\frac{n}{m}}= \sqrt[m]{x^n}$$
$$\sqrt{x}\sqrt{y}=\sqrt{xy}$$

Substitute:
$$x^{\frac{3}{2}}=\sqrt[2]{x^3}$$
$$\sqrt{x^2}\sqrt{x}=\sqrt{x^3}$$

Ans .B
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Which of the following is equal to x^(3/2)?  [#permalink]

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27 Aug 2018, 03:31
1
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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PKN

Rise above the storm, you will find the sunshine

Intern
Joined: 25 Feb 2016
Posts: 11
Re: Which of the following is equal to x^(3/2)?  [#permalink]

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27 Aug 2018, 03:44
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
Manager
Joined: 14 Feb 2016
Posts: 73
Re: Which of the following is equal to x^(3/2)?  [#permalink]

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11 Nov 2018, 12:18
1
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] 11 Nov 2018, 12:18
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