(1/2)^(-3)*(1/4)^(-2)*(1/16)^(-1)

Question

(\frac{1}{2})^{-3}(\frac{1}{4})^{-2}(\frac{1}{16})^{-1}=

(A)  (\frac{1}{2})^{(-48)}

(B)  (\frac{1}{2})^{(-11)}

(C)  (\frac{1}{2})^{(-6)}

(D)  (\frac{1}{8})^{(-11)}

(E)  (\frac{1}{8})^{(-6)}

OG 2019 #223 PS16899

Bunuel · Accepted Answer

(\frac{1}{2})^{-3}(\frac{1}{4})^{-2}(\frac{1}{16})^{-1}=2^3*4^2*16=2^3*2^4*2^4=2^{11}=(\frac{1}{2})^{-11} .

Answer: B.

BrentGMATPrepNow · Answer

Nice rule:   (\frac{a}{b})^{-n} = (\frac{b}{a})^{n}

(\frac{1}{2})^{-3}(\frac{1}{4})^{-2}(\frac{1}{16})^{-1} = (\frac{2}{1})^{3}(\frac{4}{1})^{2}(\frac{16}{1})^{1}

= (2^{3})(4^{2})(16^{1})

= (2^{3})(2^{4})(2^{4})

= 2^{11}

= (2/1)^{11}

= (1/2)^{-11}

Answer: B

Carcass · Answer

whenevr you see a fraction raised to a negative power think reciprocal

so we have : 2^3 * 4^2 * 16^1

Consolidate: 2^3 * 2^4 * 2^4

Clearly as you can see we have 2^11 only B fits

otherwise take the reciprocal of 2^11 ----> 1/2^-11

B is the best

PareshGmat · Answer

Answer = B

Keep the base as 2 & modify the powers accordingly

(\frac{1}{2})^{-3}(\frac{1}{4})^{-2}(\frac{1}{16})^{-1}

=  (\frac{1}{2})^{-3}(\frac{1}{2})^{-4}(\frac{1}{2})^{-4}

With the base the same, add the powers

-3-4-4 = -11

(\frac{1}{2})^{-11}

ScottTargetTestPrep · Answer

We start by using the negative exponent rule. When a fractional base is raised to a negative exponent, we can rewrite the expression (without the negative exponent) by flipping the fraction and making the exponent positive. For example, (1/2)^-3 = 2^3

We are using the negative exponent rule because it’s not only easier to deal with positive exponents, but also when we flip the fractional base, the fraction becomes an integer.

(1/2)^-3 = 2^3

(1/4)^-2 = 4^2 = (2 x 2)^2 = (2^2)^2 = 2^4

(1/16)^-1 = 16^1 = (2 x 2 x 2 x 2)^1 = (2^4)^1 = 2^4

We multiply each term in the expression, obtaining:

2^3 x 2^4 x 2^4

Remember, since the bases are the same, we keep the base and add the exponents. We are left with:

2^(3+4+4) = 2^11

Finally, since our answer choices are expressed in fractional form, we once again have to use the negative exponent rule. To convert a base with a positive exponent, take the reciprocal of the base and change the positive exponent to its negative counterpart. Using the rule we get:

2^11 = (1/2)^-11

The answer is B.

santro789 · Answer

I understood the method but I am just wondering if we could do this way - i tried and got the wrong answer

(1/2)^(-3)* (1/4)^(-2)*(1/16)^(-1)

= 1/(1/2)^3 * 1/(1/4)^2* 1/(1/16)^1

=1/(1/8)*1/(1/16)*1/(1/16) 
=8/1*16/1*16/1

Please let me know why cant we do this way?

Bunuel · Answer

You can and you'll get the same answer: 8/1*16/1*16/1 = 2^11 = (1/2)^(-11)

onyx12102 · Answer

where can I find similar questions?

Abhishek009 · Answer

Just click on the Tags " Exponents/Powers" you will be redirected here https://gmatclub.com/forum/search.php?s ... &tag_id=60 Hope this helps.

dabaobao · Answer

8 * 16 * 16 = 2^(3+4+4) = 2^11 = (1/2)^-11 => B

MHIKER · Answer

(\frac{1}{2})^{-3}(\frac{1}{4})^{-2}(\frac{1}{16})^{-1}=

=(\frac{1}{2})^{-3}(\frac{1}{2})^{-2*2}(\frac{1}{2})^{-4}

=(\frac{1}{2})^{(-11)}

The answer is B

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=1NIf84sA2dM

kaladin123 · Answer

The brute force approach is to immediately start simplifying the expression. This is the approach that I tried the first time.
However, a more optimum approach would be to look at the answer choices before beginning the math.

Since most of the answer choices have to deal with powers of 1/2, we are much better of simplifying the expression keeping this in mind. This helps us avoid going from a power of 1/2 to 2 and back to 1/2.

(\frac{1}{2})^{-3}(\frac{1}{4})^{-2}(\frac{1}{16})^{-1} 
 =(\frac{1}{2})^{-3}(\frac{1}{2})^{-4}(\frac{1}{2})^{-4} 
 =(\frac{1}{2})^{-3-4-4} 
 =(\frac{1}{2})^{-11}  (Option B)

Bixy34 · Answer

This is how I approached it-

-> 2^3 x 4^2 x 16^1
-> 2^3 x 2^4 x 2^4 
-> 2^11 
-> 1/2^-11

totaltestprepNick · Answer

B https://www.youtube.com/watch?v=xr4AWrxkJ9k Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

(1/2)^(-3)(1/4)^(-2)(1/16)^(-1)

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions