# Exponents

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 $x^{\frac{1}{3}}=y^{2}$, 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.

$x^{\frac{1}{3}}=y^{2}$

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.

$x^{\frac{1}{3}^{3}}=y^{2^{3}}$

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.

$x=y^{6}$

Loop back to your bottom line. You were looking for x, and you found that  $x=y^{6}$. Now look at the answer choices.

$A)y^{\frac{1}{6}}$

$B)y^{\frac{2}{3}}$

$C)y^{\frac{3}{2}}$

$D)y^{3}$

$E)y^{6}$