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Kristin Fracchia

ACT Challenge Question 1: Advanced Exponents – Explanation

Magoosh ACT Challenge Question

Here’s a refresher on our first ACT Challenge Question. If you haven’t had a chance to solve it yet, take a crack at it and then scroll down for the answer and explanation. No peeking!

ACT Challenge Question #1

Screen Shot 2015-04-17 at 2.04.00 PM


Answer and Explanation


There are two ways to solve this problem: the “math” way and the “test prep strategy” way.

Let’s talk about the test prep strategy way first. You see, this problem is a great candidate for plugging in numbers for x and y and seeing what works.

Let’s try y = 3

Therefore 2^(y+1)=2x becomes


So now we have a corresponding value for x.

When y=3, the expression in the question, 2^(y+2), equals 32. So now we have the numerical answer we are looking for in the answer choices, expressed in terms of x (which we determined equals 8.

So, plugging in 8 for x, the answer choice equivalents would be:

A. 1/1024
B. 1/19
C. 32
D. 64
E. 1024

making our answer C.

Now let’s talk about the math way:

Using the exponent rule (x^m)(x^n)=x^(m+n) we know that


so we can simplify the given equation


2^(y+2) would then be

Since we found that x=2^y we can sub in x for 2^y in the expression above and get our answer: C. 4x


About Kristin Fracchia

Kristin makes sure Magoosh's blogs are chock-full of awesome, free resources for students preparing for standardized tests. With a PhD from UC Irvine and degrees in Education and English, she’s been working in education since 2004 and has helped students prepare for standardized tests, as well as college and graduate school admissions, since 2007. She enjoys the agonizing bliss of marathon running, backpacking, hot yoga, and esoteric knowledge.

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