2. Fractional Exponents


Fractional exponents can be used instead of using the radical sign (√). We use fractional exponents because often they are more convenient, and it can make algebraic operations easier to follow.

Fractional Exponent Laws

The n-th root of a number can be written using the power 1/n, as follows:

math expression

Meaning: The n-th root of a when multiplied n times, gives us a.

a1/n × a1/n × a1/n × ... × a1/n = a

Definitions: The number under the radical is called the radicand (in the above case, the number a), and the number indicating the root being taken is called the order (or index) of the radical (in our case n).


Example

The 4-th root of 625 can be written as either:

6251/4

or equivalently, as

math expression

Its value is 5, since 54 = 625.


Raising the n-th root to the Power m

If we need to raise the n-th root of a number to the power m (say), we can write this as:

math expression

In English, this means "take the n-th root of the number, then raise the result to the power m".

 

Example 1

Simplify math expression


Here is a LiveMath document that gives us the answer.

LIVEMath


Normal answer:

Answer

Example 2

(a) Simplify math expression


Answer

(b) Simplify math expression


Answer

 

Example (3)

Simplify

math expression


Answer

 

Exercises

Q1 math expression


Answer

Q2 math expression



Answer



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