PSAT Math Multiple-Choice Question 704: Answer and Explanation

Question: 704

(6a³)³ - (2b)⁴ + c^-2 = ?

• A.
• B.
• C.
• D.

Correct Answer: D

Explanation:

(D) Take each term one at a time. When you cube 6a³, you're cubing both the 6 and the a³. When you raise an exponent to another exponent, multiply the exponents. Therefore:

(6a³)³ - (2b)⁴ + c^-2 = 216a⁹ - (2b)⁴ + c^-2

Next, raise 2b to the fourth power by raising 2 to the fourth power and raising b to the fourth power:

216a⁹ - (2b)⁴ + c^-2 = 216a⁹ - 16b⁴ + c^-2

Lastly, deal with the negative exponent. Something with a negative exponent can be rewritten by moving that something to the denominator and making the corresponding exponent positive:

Choice (D) is the correct answer.

An alternative to solving this problem to completion is to realize that once there is the 216a⁹, the answer must have this term in it. Choice (D) is the only option with this term, so you can pick it without having to do the last steps as discussed above.