# Exponents

## Link of the Day

On September 30, 1868, Louisa May Alcott published the first volume of Little Women.  The story was extremely successful and has been beloved by readers ever since.  Louisa May Alcott would make an excellent historical figure to use as an example on your SAT writing section.  You can read more about her life here, and if you have read Little Women, remember that it could make an excellent literary example too!

## 9/30 Exponents

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

Math questions need to be read just as carefully as reading questions. Avoid incomplete answers by making a note of the bottom line. Are you solving for x, or do you need the answer to 2x + 3? Assess your options for solving the problem, choose the most efficient method, and attack the problem! Once you have the answer, loop back to verify that it addresses the bottom line.

If , which of the following expresses a in terms of b?

Bottom line: This question asks you to solve for the variable a.

Assess your options: You could try to plug in the answer choices for a and choose a number for b to try to find the answer. However, that method requires you to work several problems and includes multiple steps. Instead, use algebra to rearrange the equation.

Attack the problem: You see two numbers with exponents. When two bases are the same, then the exponents can be set equal to each other. Your two bases are 2 and 4. How can you make both bases the same? Use the fact that 2² = 4 by plugging that into your equation.

$2^{a} = 4^{b}$

$2^{a} = 2^{2b}$

Now you can ignore the bases and set the exponents equal to each other. You now have:

a = 2b

Loop back: The question asked you to find a in terms of b, and that is just what you did. Look down at your answer choices

(A)

(B) b

(C) 2b

(D) 4b
(E)

The correct answer is (C).

On sat.collegeboard.org, 54% of the responses were correct.

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