SOLUTION: simplify the expression. Write the result using positive exponents only. 8^-1 + 6^-1

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Question 68787: simplify the expression. Write the result using positive exponents only.
8^-1 + 6^-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Any base with a negative exponent simply means it needs to be inverted. So 2%5E-4 becomes 1%2F2%5E4. To remember this, imagine a number line which represents the exponent. For example "1" represents 2%5E1, "2" represents 2%5E2, "3" represents 2%5E3, etc. When you go backwards, the opposite operation is applied. Instead of multiplication, division is performed on the base. So to get to 2%5E0, start at 2%5E1 and divide by 2, and you'll get 2%2F2=2%5E0 which equals 1. This explains why x%5E0=1 x is true for any number since any number divided by itself is 1. To get to 2%5E-1 divide by 2 again.

number_line%28+987%2C+-3%2C+3%29
2%5E-2=1%2F2%5E2<---------------2%5E-1=1%2F2%5E1<----------2%5E0=2%2F2=1 --------------->2%5E1=2--------------->2%5E2=4


Going Backwards: Divide base by itself<--------------->Going forwards: Multiply base by itself

Now that you have a better understanding of negative exponents, you can simplify 8%5E-1%2B6%5E-1 by simply inverting the bases to get 1%2F8%5E1%2B1%2F6%5E1