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Exponents

Dividing Terms with the Same Base

When one term is divided by another with the same base, we subtract exponents:

b^m/b^n=b^m*b^(-n)=b^(m-n).






This is true for all kinds of exponents, positive and negative (and as we will see later, fractional).


Example 4A

2^7/2^3=2^(7-3)=2^4.

x^5/x^3=x^(5-3)=x^2.

y^3/y^7=y^(3-7)=y^(-4)=1/y^4.

a^2/a^(-4)=a^(2-(-4)=a^(2+4)=a^6.


Study some more worked examples:

               
 
 
 
   

=
x
=
=
               
               

 

Exercise 4A.

Now practice with some of the following exercises:

   
 

=
 
 

Example 4B.

What if we have terms that are both in a product and quotient with the same base? We had the exponents in the numerator and divide those in the denominator. Check out these examples:

(x^2*x^4)/(x^3*x*x^5)=x^(2+4-3-1-5)=x^(-3)=1/x^3.

(y^(-2)*y*y^4)/(y^5*y^(-3))=y^(-2+1+4-5-(-3))=y^1=y.

(a^3*c^2*b^5*b*a)/(b^2*b^4*c^3)=a^(3+1)*b^(5+1-2-4)*c(2-3)=a^4*b^0*c^(-1)=a^4/c.


Exercise 4B

Got that? Then test yourself with these harder exercises:


Simplifies to
a
b
c

<< Multiplying Terms with the Same Base | Exponents Index | Raising One Power to Another >>

 

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