If x ≠ 0, what is the value of (x^m/x^n)^p ?

Question

If  x ≠ 0 , what is the value of  (\frac{x^m}{x^n})^p  ?

(1)  p = 1

(2)  m = n

Mona2019 · Answer

Statement B is sufficient 
If m=n,m-n =0
So x^((m-n)*p)=x^0=1

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TestPrepUnlimited · Answer

(\frac{x^m}{x^n})^p = x^{(m -n)*p} .

Statement 1 is insufficient.

Statement 2 makes the exponent  (m - n)* p = 0 , thus x will have a power of 0 and the value of the expression would be 1, sufficient.

Ans: B

MathRevolution · Answer

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

The first step of the Variable Approach: The first step and the priority is to modify and recheck the original condition and the question to suit the type of information given in the condition.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Learn the 3 steps. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find the value of \((\frac{(x^m)}{(x^n)})^p\) - where 'x' ≠ 0

=> \((\frac{(x^m)}{(x^n)})^p\) = \(((x)^{m-n})^p\)

Condition(1) tells us that p = 1.

=> We still don't have any values of 'm' and 'n'.

Since the answer is not unique , condition(1) alone is not sufficient by CMT 2.

Condition(2) tells us that m = n .

=> \(((x)^{m-n})^p\) = \(((x)^{m-m})^p\) = \(((x)^{0})^p\) = \((x)^0\) = 1

Since the answer is unique , condition(2) alone is sufficient by CMT 2.

Condition(2) alone is sufficient.

So, B is the correct answer.

Answer: B

SAVE TIME: By Variable Approach[MODIFICATION], check the condition quickly and separately and mark answer as A or B.

hellypatel · Answer

does not matter what is the value of X according to statement 2, X^n/X^m = 1,

if only statement 2 then, (X^n/X^m)* P= 1*p

therefore the value of p also matters
so the answer is C

Bunuel 
please help me, am i wrong?

Bunuel · Answer

Please read the previous responses. It's (x^m/x^n)^p, not (x^m/x^n)*p.

hellypatel · Answer

ooh thanks, but if its (x^m/x^n)*p then answer would C?

If x ≠ 0, what is the value of (x^m/x^n)^p ?

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GMAT Data Sufficiency (DS) Questions

If x ≠ 0, what is the value of (x^m/x^n)^p ?

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