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A fractional exponent is a way of combining powers and roots in a single expression.
A fractional exponent has the following general form:
b n/m = (m√b) n = m √ (b n)
Question 1: How to calculate fractional exponents?
To calculate the fractional exponent we check the fraction given in power form. Then, break the fraction n/m in two terms
Then the fraction part changes to mth root of that number and n is its power.
b n/m = (m√b) n = m √ (b n)
Example:
5 5/3 = (5^5)5/3 = 3√(5^5) = 5 x 3√(5^2) = 53√25
Question 2: How to multiply fractional exponents?
Multiplying words with the same base and fractional exponents is the same as adding the exponents together.
Example
51/2 x 53/2 = 51/2+3/2 = 54/2 = 52 = 25
Question 3: How to work out negative fractional indices?
To solve the negative exponent fraction indices we use the following rule x-nm=1xnm=1mxn.
Example:
2-5/2 = 1/(2)5/2 = 1/√25 = 1/(2x2x√2) = 1/(4√2)
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