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

Question

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

(A)  x^2 \sqrt{x}

(B)  x \sqrt{x}

(C)  \sqrt {x^2}

(D)  \sqrt {x}

(E)  (x^3)^2

PKN · Answer

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

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

Ans. (B)

StudiosTom · Answer

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

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

Ans .B

PKN · Answer

Hi onyx12102 , You must know the following basic rules of exponents and roots:- 1) Fraction as a power:- a^{\frac{1}{n}}=\sqrt {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 {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.

onyx12102 · Answer

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

CLIMBTHELADDER · Answer

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

Sugoisweet · Answer

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

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

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

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