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Exponents

Multiplying Terms with the Same Base

When two terms with the same base b are multiplied, we add their exponents:

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 3A

3^2*3^4=(3*3)*(3*3*3*3)=3^6=3^(2+4).

x^3*x^4=x^(3+4)=x^7.

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

y^(-5)*y^(-3)=y^(-5+(-3))=y^(-8).


Want to see more? Click on "New Example":

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Exercise 3A.

Practice makes perfect! So try some of the following exercises. Keep clicking "New Exercise" and solving until you feel confident:


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Example 3B.

This rule applies no matter how many terms are in the product, as long as they have the same base:

=x^2*x^5*x^3=x^(2+5+3)=x^10.

x^(-8)*x^2*x^3=x^(-8+2+3)=x^(-3)=1/x^3.

What if we have more than one base in the same product? Just add the powers of those with the same base!

x^3*y^5*x^3=x^(3+3)*y^5=x^6*y^5.

a^3*a^2*c*b^4*c^3*b^3*a^5=a^(3+2+5)*b^(4+3)*c^(1+3)=a^10*b^7*c^4.

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


Exercise 3B.

Got it? Feeling confident? Then here are some harder exercises to test your skills:

Simplifies to
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<< Negative Exponents | Exponents Index | Dividing One Term by Another with the Same Base >>

 

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