Raising a value to the power??? You should deal with the negative sign first, then use the rule for the fractional exponent. Dealing with fractional exponents. The rule for fractional exponents: When you have a fractional exponent, the numerator is the power and the denominator is the root.
I'm krista. Changing fractional exponents into roots and vice versa. Take the course Want to learn more about Algebra 2? I have a step-by-step course for that. Learn More. An example where we change the fractional exponent into a root in order to simplify the expression Example Simplify the expression.
Exponents show the number of times a number is replicated in multiplication. Here, exponent 2 is a whole number. Fractional exponents are ways to represent powers and roots together. In any general exponential expression of the form a b , a is the base and b is the exponent.
When b is given in the fractional form, it is known as a fractional exponent. There are certain rules to be followed that help us to multiply or divide numbers with fractional exponents easily.
Many people are familiar with whole-number exponents, but when it comes to fractional exponents, they end up doing mistakes that can be avoided if we follow these rules of fractional exponents. These rules are very helpful while simplifying fractional exponents.
Let us now learn how to simplify fractional exponents. Simplifying fractional exponents can be understood in two ways which are multiplication and division.
It involves reducing the expression or the exponent to a reduced form that is easy to understand. Let us understand the simplification of fractional exponents with the help of some examples. In this example, both the base and the exponent are in fractional form. To multiply fractional exponents with the same base, we have to add the exponents and write the sum on the common base. Here, we have to subtract the powers and write the difference on the common base.
Here, we are dividing the bases in the given sequence and writing the common power on it. Negative fractional exponents are the same as rational exponents.
You'll get the same result either way. So you could start by taking the 3rd root of 8, which is 2, and then raising that to the 2nd power, which would give you 4. Or you could start by raising 8 to the 2nd power, which equals 64, and then taking the 3rd root of that number, which is 4.
Same result. In fact, the rule of "numerator as power, denominator as root" applies to all exponents -- even whole-number exponents and fractional exponents with a numerator of 1. Raising 9 to the 2nd power gives you Now you have to get the "1st root" of But the 1st root of any number is the number itself, so the answer remains You could start by raising 9 to the "1st power.
So all you have to do is get the square root of 9, which is 3. The rule still applies, but in these situations, you can skip a step. Cam Merritt is a writer and editor specializing in business, personal finance and home design.
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