Return to the Purplemath home page

 


powered by FreeFind

 

Print-friendly page

 

 

Simplifying Expressions with Exponents (page 1 of 3)

To simplify with exponents, don't feel like you have to work directly from the rules. It is often simpler to work directly from the definition and meaning of exponents. For instance:

  • Simplify x6 × x5

    • The rules tell me to add the exponents. But I had trouble keeping the rules straight in the beginning, so I just thought about what exponents mean. The "x6" means "six copies of x multiplied together", and the "x5" means "five copies of x". So if I multiply them together, I've got eleven copies of x multiplied together. Then:

      x6 × x5 = x11

  • Simplify the following expression:

      • 6^8 / 6^5

    The exponent rules tell me to subtract the exponents. But say I've forgotten the rules again. The "68" means I have eight copies of 6 on top; the "65" means I have five copies of 6 underneath.

      (6×6×6×6×6×6×6×6) / (6×6×6×6×6)

    How many extra 6's do I have, and where are they? I have three extra, and they're on top. Then:

      (6×6×6) / 1 = 6^3

  • Simplify the following expression:

      • t^10 / t^8

    How many extra copies of t do I have, and where are they? I have two extra copies, on top:

      (t×t)/1 = t^2

  • Simplify the following expression: Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

      • 5^3 / 5^9

    How many extra copies of 5 do I have, and where are they? I have six extra copies, underneath:

      1/(5×5×5×5×5×5) = 1 / 5^6

Note: If you apply the subtraction rule, you'll end up with 53–9 = 5–6, which is mathematically correct, but is almost certainly not the answer they're looking for. Whether or not you've been taught about negative exponents, when they say "simplify", they mean "so it doesn't have negative powers". Some students will try to get around this minus-sign problem by arbitrarily switching the sign to magically get "56" on top (rather than below a "1"), but this is incorrect. Don't do this.

  • Simplify the following expression:

      • (5x^5) / (3x^3)

    Don't forget that the "5" and the "3" are just numbers. Since 3 doesn't go evenly into 5, I can't cancel the numbers. Don't try to subtract the numbers, because the 5 and 3 in " 5/3 " are not the same as the 5 and 3 in " x5 / x3 ". The 5/3 stays as it is.

    For the variables, I have two extra copies of x on top, so the answer is:

      (5xx) / 3 = (5x^2) / 3 = (5/3)x^2

Either of the purple highlighted answers is acceptable; the only difference is in the formatting; they mean the same thing.

  • Simplify (–46x2y3z)0

    • This is simple enough: anything to the zero power is just 1.

      (–46x2y3z)0 = 1

  • Simplify –(46x2y3z)0

    • The parentheses still simplifies to 1, but this time the "minus" is out front so the exponent doesn't touch it. So the answer is:

      –(46x2y3z)0 = –1

  • Simplify the following expression:

      • (15a^5 b^2 c^4) / (25a^3 b^3 c^4)

    I can cancel off the common factor of 5 in the number part of the fraction:

      (3a^5 b^2 c^4) / (5a^3 b^3 c^4)

    Now I need to look at each of the variables. How many extra of each do I have, and where are they? I have two extra a's on top. I have one extra b underneath. And I have the same number of c's top and bottom, so they cancel off entirely. This gives me:

Top  |  1 | 2 | 3  |  Return to Index  Next >>

Cite this article as:

Stapel, Elizabeth. "Simplifying Expressions with Exponents." Purplemath. Available from
    http://www.purplemath.com/modules/simpexpo.htm. Accessed
 

 

Lessons index

Lessons CD

Purplemath:
  Linking to this site
  Printing pages
  Donating
  School licensing

Reviews of
Internet Sites:
   Free Help
   Practice
   Et Cetera

The "Homework
   Guidelines"

Study Skills Survey

Tutoring ($$)

This lesson may be printed out for your personal use.

Content copyright protected by Copyscape website plagiarism search
  

  Copyright © 2006-2008  Elizabeth Stapel   |   About   |   Terms of Use

 

 Feedback   |   Error?