document.write( "Question 201368: Write the expression using exponent notation. sq.rt. 5z \n" ); document.write( "
Algebra.Com's Answer #151587 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
By definition \"sqrt%285z%29+%2A+sqrt%285z%29+=+5z\"


\n" ); document.write( "Writing this in exponential form, using \"y\" for the exponent we will figure out, we get:
\n" ); document.write( "\"%285z%29%5Ey+%2A+%285z%29%5Ey+=+%285z%29%5E1\"


\n" ); document.write( "The rule for exponents, when we multiply, is to add the exponents. So we get:
\n" ); document.write( "\"%285z%29%5E%28y%2By%29+=+%285z%29%5E1\"
\n" ); document.write( "which simplifies to:
\n" ); document.write( "\"%285z%29%5E%282y%29+=+%285z%29%5E1\"
\n" ); document.write( "This means that
\n" ); document.write( "2y = 1
\n" ); document.write( "Dividing both sides by 2:
\n" ); document.write( "\"y+=+1%2F2\"
\n" ); document.write( "


\n" ); document.write( "Therefore \"sqrt%285z%29+=+%285z%29%5E%281%2F2%29\"

Using similar logic we can show that \"root%283%2C+x%29+=+x%5E%281%2F3%29\"
\n" ); document.write( "\"root%284%2C+x%29+=+x%5E%281%2F4%29\"
\n" ); document.write( "\"root%285%2C+x%29+=+x%5E%281%2F5%29\"
\n" ); document.write( "etc. \n" ); document.write( "

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