Last Updated on May 5, 2023
GMAT OFFICIAL GUIDE PS –
Solution:
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
Answer: B
