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Exponents

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


Remember to follow the Knowsys Method: read carefully, identify the bottom line, assess your options, attack the problem, and loop back to ensure that you answered the question correctly.

If , which of the following must be equivalent to x?

After reading, find the bottom line and note it at the top of your scratch work.

x=?

Next, assess your options. There are two courses of action apparent here: you could pick numbers and plug them into x and y, or you could apply the exponent rules to solve for x. Which would be faster and easier? The exponent rules.



What can you do here? Since you need to isolate x, pay attention to its exponent. Normally, a fraction in an exponent indicates that you need to take a root--in this case, a cube root--but since you cannot take the root of a variable, do the opposite. Cube both sides.



The rule for "power to a power" situations, when an exponent is itself the base of another exponent, is to simply multiply the powers together.



Loop back to your bottom line. You were looking for x, and you found that  . Now look at the answer choices.












The answer is E.


On sat.collegeboard.org, 50% of responses were correct.


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