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Law of Rational Exponents

TopAn exponent shows the multiplication of the number of identical factors like 53 and can be rewritten as
(5) * (5) * (5) means three identical factors of the number 5. Exponent is the first operation so this is applicable only if it is attached with a number like 4x3 is 4 (x) (x) (x), it is not like that (4x) * (4x) * (4x).
For example 32 can be written as 25.
Law of Rational Exponents is same as the law of Integer exponents. Here is a review of law of rational exponents,
The product law is,
(xa) * (xb) = xa + b,
If there is a power to a power then,
(xa)b = xab,
If there is a product to a power then
(xy)a = xa * ya,
The quotient rule is
xa / xb = xa – b,
The quotient rule to a power
(x/y)a = xa / ya,
All the exponents can be written as in the form of Radicals, so first there is need for a conversation of a rational exponent to a radical. There is a n example provided the conversation of the rational exponent in to the radical form
Example: Convert it into the radical 25( ½ )?
To convert a rational exponent to a radical exponent the denominator becomes the index and the numerator of the exponent stays with the variable and is in the radical form as
25( ½ ) = √25
Some steps are there to solve the expression with the ration exponent
First need to find the prime factors.
Then need to express them into exponent form.
Then the multiplication rule is applied.
Then simplification of the exponent and conversion from the exponent to the ordinary form takes place.