ACT Math Test : Exponents & Roots
Study concepts, example questions & explanations for ACT Math Test
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Example Questions
Example Question #4 : Fundamental Properties Of Roots & Exponents
It is important to be able to convert between root notation and exponent notation. The third root of a number (for example, 
So when you see that you're taking the third root of 
This then allows you to apply the rule that when you take one exponent to another power, you multiply the powers:
This then means that you can express this as:
Example Question #31 : Exponents & Roots
With roots, it is important that you are comfortable with factoring and with expressing roots as fractional exponents. A square root, for example, can be expressed as taking that base to the 
This would allow you to then add the exponents and arrive at:
Since that 2 in the denominator of the exponent translates to "square root," you would have the square root of 
If you were, instead, to work backward from the answer choices, you would see that answer choice 
You can express that as:
That in turn will factor to:
The first root then simplifies to 
Therefore, as you can see, choice 
Example Question #31 : Exponents & Roots
Which of the following is equal to 
Simplify each of the expressions to determine which satisfies the condition of the problem:
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