document.write( "Question 68787: simplify the expression. Write the result using positive exponents only.
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Algebra.Com's Answer #48976 by jim_thompson5910(35256) $\"\"$ $\"About$

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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. \r
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\n" ); document.write( "\n" ); document.write( " $\"number_line%28+987%2C+-3%2C+3%29\"$
$\"2%5E-2=1%2F2%5E2\"$ <--------------- $\"2%5E-1=1%2F2%5E1\"$ <---------- $\"2%5E0=2%2F2=1\"$ ---------------> $\"2%5E1=2\"$ ---------------> $\"2%5E2=4\"$
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\n" ); document.write( "Going Backwards: Divide base by itself<--------------->Going forwards: Multiply base by itself\r
\n" ); document.write( "\n" ); document.write( "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 $\"1%2F8%5E1%2B1%2F6%5E1\"$
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