# Exponents

Pursuing your dreams takes dedication, particularly when you have to juggle athletic training and school at the same time. 16-year-old Olympic athlete Ariel Hsing has been dreaming of playing table tennis in the Olympics since she was just 8 years old. Her talent and dedication to her sport have helped to make that dream a reality. However, she understands that table tennis is not as popular as other sports (and therefore the endorsements are less lucrative). In addition to striving for Olympic greatness, Hsing also aspires to attend Stanford. You can read more about Ariel Hsing here. Her dedication to both her sport and her academics make her a great "Excellent Example" for your essay.

## 7/17 Exponents

Read the following SAT test question and then select the correct answer.

As always, remember to follow the Knowsys method for math. Read the problem carefully and identify the bottom line (what you are looking for). Then, consider your options. How could you solve it? How should you solve it? Next, attack the problem using the method that you selected. Finally, loop back and verify that your answer matches the bottom line.

If  and , and if , which of the following is true?

The key to this question is to know your exponent rules and follow the Knowsys method for math. Start by reading the problem carefully and identifying the bottom line. If you glance at the answers below, you can see that you are looking for the relationship between x and y. Now, consider your options. What could you do? What should you do? Since you only have two variables in the equation (x and y), all you need to do is simplify the equation. Next, attack the problem using the method you have selected. You want to simplify the equation and move x and y out of the exponents. In order to do that, you need matching bases.  Using your exponent rules you can rewrite the equation as follows

$3^{2x}=27^{2y}\Rightarrow 3^{2x}=(3^{3})^{2y}\Rightarrow 3^{2x}=3^{3*2y}\Rightarrow 3^{2x}=3^{6y}$

Since the bases are the same, you can just eliminate them and you are left with

$3^{2x}=3^{6y} \Rightarrow 2x=6y$

Now, do a little basic algebra to simplify and get

$2x=6y \Rightarrow x=3y$

The final step in the Knowsys method for math is to loop back and verify that your answer matches the bottom line. Since you have followed all the algebra rules, you know that your equation is true. Look at the answers below and choose the one that matches your prediction.

(A) x=y
(B) x=2y
(C) 2x=y
(D) x=3y
(E) 3x=y

The correct answer choice is (D).

On sat.collegeboard.org 51% of the responses were correct.

For more help with math, visit www.myknowsys.com.