PSAT Math Multiple-Choice Question 220: Answer and Explanation

Question: 220

What is the value of ?

• A. 9⁶⁰
• B. 9¹²⁰
• C. 9¹⁵⁰
• D. 9²¹⁰

Correct Answer: D

Explanation:

D

Difficulty: Hard

Category: Passport to Advanced Math/Exponents

Getting to the Answer: The numbers in some questions are simply too large to use a calculator (you get an "overflow" error message). Instead, you'll have to rely on rules of exponents. Notice that all of the base numbers have 3 as a factor, so rewrite everything in terms of 3. This will allow you to use the rules of exponents. Because 27 is the cube of 3, you can rewrite 27⁹⁰ as a power of 3:

Now, the product should read: 3⁹⁰ × 3²⁷⁰, which is equal to 3^{90 + 270} = 3³⁶⁰. Repeat this process for the quantity that is being divided:

Finally, use rules of exponents one more time to simplify the new expression:

All the answer choices are given as powers of 9, so rewrite your answer as a power of 9:

Choice (D) is correct.