document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=430116>Question 430116</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rewrite & simplify the given expression using positive exponents only.<BR>\n" );
document.write( "(square root x^-5 + x^-5y^7z^-2)(x^9y^-2z^9)<BR>\n" );
document.write( "Only x^-5 is a square root </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #298698 by </B><A HREF=/tutors/aboutme.mpl?userid=haileytucki><B>haileytucki(390)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=haileytucki><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=haileytucki><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=298698\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ~ = square root of in this answer\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(~(x^(-5))+x^(-5)y^(7)z^(-2))(x^(9)y^(-2)z^(9))\r<BR>\n" );
document.write( "\n" );
document.write( "Pull all perfect square roots out from under the radical.  In this case, remove the x^(-3) because it is a perfect square.<BR>\n" );
document.write( "(x^(-3)~(x)+x^(-5)y^(7)z^(-2))(x^(9)y^(-2)z^(9))\r<BR>\n" );
document.write( "\n" );
document.write( "Move all negative exponents from the numerator to the denominator and make the exponents positive.  A negative exponent follows the rule: a^(-n)=(1)/(a^(n)).<BR>\n" );
document.write( "(x^(-3)~(x)+(y^(7))/(x^(5)z^(2)))(x^(9)y^(-2)z^(9))\r<BR>\n" );
document.write( "\n" );
document.write( "Remove the negative exponent in the numerator by rewriting x^(-3)~(x) as (~(x))/(x^(3)).  A negative exponent follows the rule: a^(-n)=(1)/(a^(n)).<BR>\n" );
document.write( "((~(x))/(x^(3))+(y^(7))/(x^(5)z^(2)))(x^(9)y^(-2)z^(9))\r<BR>\n" );
document.write( "\n" );
document.write( "To add fractions, the denominators must be equal.  The denominators can be made equal by finding the least common denominator (LCD).  In this case, the LCD is x^(5)z^(2).  Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.<BR>\n" );
document.write( "((~(x))/(x^(3))*(x^(2)z^(2))/(x^(2)z^(2))+(y^(7))/(x^(5)z^(2)))(x^(9)y^(-2)z^(9))\r<BR>\n" );
document.write( "\n" );
document.write( "Complete the multiplication to produce a denominator of x^(5)z^(2) in each expression.<BR>\n" );
document.write( "((x^(2)z^(2)~(x))/(x^(5)z^(2))+(y^(7))/(x^(5)z^(2)))(x^(9)y^(-2)z^(9))\r<BR>\n" );
document.write( "\n" );
document.write( "Combine the numerators of all expressions that have common denominators.<BR>\n" );
document.write( "((x^(2)z^(2)~(x)+y^(7))/(x^(5)z^(2)))(x^(9)y^(-2)z^(9))\r<BR>\n" );
document.write( "\n" );
document.write( "Remove the negative exponent in the numerator by rewriting x^(9)y^(-2)z^(9) as (x^(9)z^(9))/(y^(2)).  A negative exponent follows the rule: a^(-n)=(1)/(a^(n)).<BR>\n" );
document.write( "((x^(2)z^(2)~(x)+y^(7))/(x^(5)z^(2)))((x^(9)z^(9))/(y^(2)))\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply ((x^(2)z^(2)~(x)+y^(7)))/(x^(5)z^(2)) by (x^(9)z^(9))/(y^(2)) to get (x^(4)z^(7)(x^(2)z^(2)~(x)+y^(7)))/(y^(2)).<BR>\n" );
document.write( "((x^(4)z^(7)(x^(2)z^(2)~(x)+y^(7)))/(y^(2)))\r<BR>\n" );
document.write( "\n" );
document.write( "Remove the parentheses around the expression (x^(4)z^(7)(x^(2)z^(2)~(x)+y^(7)))/(y^(2)).<BR>\n" );
document.write( "(x^(4)z^(7)(x^(2)z^(2)~(x)+y^(7)))/(y^(2)) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );