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The fraction in an exponent takes the base to that radical power (1/2 is take the square root, 1/3 is take the third or "cube" root, 1/5 is take the fifth root, etc) and the numerator to that positive power (2 is squared, 3 is cubed, etc)
For example:
4 to the 1/2 power is the square root of 4, which is two.
4 to the 3/2 power is the square root of four, 2, taken to the third power, which is 8.
Sources: Background Knowledge
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What is the reciprocal of a negative exponent when the exponent is a fraction?
The reciprocal of a^(-x/y) is 1/a^(x/y). The fact that the exponent is a fraction makes no difference.
Why do you move a negative exponent to the other side of the fraction?
This is a procedure used to help people who are new to negative exponents. A negative exponent, when moved to the other side of the fraction, becomes a positive exponent and beginners are more comfortable with working with positive fractions.
Multiply a number by a fraction exponent?
(16n^8)^3/2
What is the Definition of negative exponents?
A negative exponent simply means that the base is on the wrong side of the fraction line.For example, if you have x-2, you can turn this into a positive exponent by moving the base to the denominator and changing the sign on the exponent. The result would be:1--x2
What does a negative exponent mean?
"Dose" is a measured portion of a medicine. I am not aware of any exponents that have anything to do with measured quantities of medication! A negative exponent is simply the reciprocal of the corresponding positive exponent. Thus x^(-a) = (1/x)^a for non-zero x.
