ACT and SAT Math Tips: Fractional Exponents

The ACT and SAT use exponents and roots on the tests to assess your ability to manipulate expressions. Most students think, “No problem! That’s why I have a fancy schmancy calculator!” but the test makers often use your calculator against you. The questions they serve up will likely involve variables so that your calculator is rendered helpless and any time you spend reaching for it results in precious, wasted seconds.

So it is imperative that you know your formulas for exponents and roots and be comfortable using them. One fairly common question type involves fractional exponents, which are root questions in disguise:

To help you remember this formula, think of the fractional exponent as a pesky weed that must be removed from the garden. It takes power to pull the greens growing above ground, and the root of the weed is below ground. If you think of the ground as the fraction bar, you will always remember that the power is above and the root is below:

If faced with a fractional exponent and you forget what the numerator and denominator mean, remember the weed:

Note, however, that if a variable with a fractional exponent is raised to another power, you may not have to convert the expression into root form. The exponents are multiplied, and often simplified into a single whole number exponent:

If you need more tips and tricks, be sure to check out our ACT courses!

Photo: “Calculator Closeup,” courtesy of Kurt Nordstrom