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Exponents

General Fractional Exponents

Let b be a positive number, and m and n positive integers. We define

b^(m/n)=(b^(1/n))^m.

 

 

 

This agrees with Raising an exponent to a higher power.

Examples

Click on the question marks below to see these examples step-by-step.

4^(3/2) =(4^(1/2))^3 =2^3 =8.

32^(4/5) =(32^(1/5))^4 =2^4 =16.

More Examples

Exercise

Got it? Good. Then try some of these exercises to test your skills.

b x bx

Just as for any integer number x, it is true that for any fractional number x,

b^(-x)=1/b^x.

Example

Click the question marks to see this example step-by-step:

8^(-2/3) =1/(8^(2/3)) =1/(8^(1/3)^2) =1/2^2 =1/4.

More Examples

Exercise

Test your skills with these exercises:

b x bx

All of the rules of integer exponents hold for fractional exponents.

Example

(b^(3/2))/(b^(1/2))=b^(3/2-1/2)=b^1=b.

(3*a^(3/2)*b)^2*(-a^2*b^3)=9*a^3*b^2*(-a^2*b^3)=-9*a^5*b^5.

(sqrt(9*x^2*y^6))/((8*x^3*y^9)^(1/3))=(3*x*y^3)/(2*x*y^3)=3/2.


Have a look at a few more examples.

 
(
a
b
c
)

 
(
a
b
c
)

 

Simplifies to
a
b
c

 

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