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Multiplying Exponents

Introduction

Multiplying exponents is quite straightforward. When the bases are the same, we simply add the first exponent to the second exponent.

Terms

Exponent - The number of times to multiply the base.
Base - The number being multiplied.

Lesson

To multiply exponents with the same base, we add all the exponents together. For example, if we are given 26∗222^6 * 2^2, we add the exponents – 6+2=8 and we are left with 282^8 or 256 (evaluated).

Here is another example:

33∗34=33+4=37=21873^3 * 3^4 = 3^{3+4} = 3^7 = 2187

Examples

Multiplying Exponents (Example #1)

x2x−1x−2x^{2}x^{-1}x^{-2}
When multiplying exponents with the same base, you add the exponents
x2x−1x−2=x2−1−2x^{2}x^{-1}x^{-2} = x^{2-1-2}
x2−1−2=x−1x^{2-1-2} = x^{-1}

Multiplying Exponents (Example #2)

s1s2s3s^{1}s^{2}s^{3}
When multiplying exponents with the same base, you add the exponents
s1s2s3=s1+2+3s^{1}s^{2}s^{3} = s^{1+2+3}
s1+2+3=s6s^{1+2+3} = s^{6}

Multiplying Exponents (Example #3)

4−2414^{-2}4^{1}
When multiplying exponents with the same base, you add the exponents
4−241=4−2+14^{-2}4^{1} = 4^{-2+1}
4−2+1=4−14^{-2+1} = 4^{-1}

Multiplying Exponents (Example #4)

353−1323^{5}3^{-1}3^{2}
When multiplying exponents with the same base, you add the exponents
353−132=35−1+23^{5}3^{-1}3^{2} = 3^{5-1+2}
35−1+2=363^{5-1+2} = 3^{6}

Multiplying Exponents Worksheets (PDF)