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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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New post 26 Aug 2018, 20:11
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

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

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

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New post 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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New post 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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New post 27 Aug 2018, 03:31
1
onyx12102 wrote:
PKN
Please simplify your answer by showing how

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
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.
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PKN

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

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

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New post 11 Nov 2018, 12:18
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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] 11 Nov 2018, 12:18
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