document.write( "Question 404628: how do i simplify this without using zero or negative integers as exponents?\r
\n" ); document.write( "\n" ); document.write( "{ab^2c^-2}^-3 \n" ); document.write( "

Algebra.Com's Answer #285948 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%28a%2Ab%5E2%2Ac%5E%28-2%29%29%5E%28-3%29\"$
\n" ); document.write( "With these problems I like to simplify first. Sometimes the process of simplification causes the zero and/or negative exponents to disappear on their own. After simplifying, if there are still zero or negative exponents, then handle that at the end.

\n" ); document.write( "So we'll start with simplifying. The rule for exponents for this type of expression is $\"%28p%2Aq%29%5Ez+=+p%5Ez%2Aq%5Ez\"$
\n" ); document.write( "Applying this rule to your expression we get:
\n" ); document.write( " $\"%28a%29%5E%28-3%29%2A%28b%5E2%29%5E%28-3%29%2A%28c%5E%28-2%29%29%5E%28-3%29\"$
\n" ); document.write( "The rule for a power of a power is to multiply the exponents:
\n" ); document.write( " $\"%28a%29%5E%28-3%29%2A%28b%5E%282%2A%28-3%29%29%29%2A%28c%5E%28%28-2%29%2A%28-3%29%29%29\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"a%5E%28-3%29%2Ab%5E%28-6%29%2Ac%5E6\"$
\n" ); document.write( "We're done simplifying. Now we'll address the negative exponents that remain. In general $\"p%5E%28-n%29+=+1%2Fp%5En\"$ . Using this pattern on the negative exponents in your expression we get:
\n" ); document.write( " $\"%281%2Fa%5E3%29%2A%281%2Fb%5E6%29%2Ac%5E6\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"c%5E6%2F%28a%5E3%2Ab%5E6%29\"$ \n" ); document.write( "

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