SOLUTION: 1/X^8 * x^5

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Question 203213This question is from textbook algebra 1
: 1/X^8 * x^5

This question is from textbook algebra 1

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
There are a couple of ways you can solve this:
  1. Multiply and then simplify:
    1. Make a fraction out of x%5E5:
      %281%2Fx%5E8%29+%2A+x%5E5+=+%281%2Fx%5E8%29+%2A+%28x%5E5%2F1%29
    2. Multiply the fractions:
      %281%2Fx%5E8%29+%2A+%28x%5E5%2F1%29+=+x%5E5%2Fx%5E8
    3. Simplify
      • If you know about negative exponents you can simply use the rule for division with exponents: x%5Ea%2Fx%5Eb+=+x%5E%28a-b%29:
        x%5E5%2Fx%5E8+=+x%5E%285-8%29+=+x%5E%28-3%29
      • If you do not know about negative exponents, then factor and cancel common factors:
        Since x%5E%28-3%29+=+1%2Fx%5E3 these answers are the same.
  2. Eliminate the fraction first and then multiply
    1. Rewrite 1%2Fx%5E8 with a negative exponent:
      %281%2Fx%5E8%29+%2A+x%5E5+=+x%5E%28-8%29+%2A+x%5E5
    2. Multiply using the rule for multiplication with exponents: x%5Ea+%2A+x%5Eb+=+x%5E%28a%2Bb%29:
      x%5E%28-8%29+%2A+x%5E5+=+x%5E%28-8+%2B+5%29+=+x%5E%28-3%29