document.write( "Question 346277: how do i evaluate the expression 5x3 to the negative 3rd power? \n" ); document.write( "

Algebra.Com's Answer #247646 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
I think you mean \"How do I simplify...\". Evaluating is when you replace one or more variables with numbers and then simplify. There are no variables in your expression.

\n" ); document.write( " $\"5%2A3%5E%28-3%29\"$
\n" ); document.write( "Accorsing to the order of operations (aka PEMDAS), we should simplify exponents before mutiplying. In order to raise 3 to the -3 power we need to remember what a negative exponent means. A negative exponent means a reciprocal. In general:
\n" ); document.write( " $\"x%5E%28-n%29+=+%28x%2F1%29%5E%28-n%29+=+1%2Fx%5En\"$
\n" ); document.write( "So 3^(-3) = 1/3^3 = 1/3*3*3 = 1/27. So we can replace $\"3%5E%28-3%29\"$ with 1/27:
\n" ); document.write( " $\"5%2A%281%2F27%29\"$
\n" ); document.write( "Now we can multiply:
\n" ); document.write( " $\"5%2F27\"$
\n" ); document.write( "And we're finished. \n" ); document.write( "

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