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

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

Answer: B.
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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
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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
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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

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

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.
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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?

You can and you'll get the same answer: 8/1*16/1*16/1 = 2^11 = (1/2)^(-11)
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where can I find similar questions?

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

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

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

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

The answer is B
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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1

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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)
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