document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85206>Question 85206</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618163832/algebrahomeworkh>ALGEBRA 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> WHAT IS THE (X^4Y^8)^1/2*(X^1/2)6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61413 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=61413\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "(X^4Y^8)^1/2*(X^1/2)6<BR>\n" );
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document.write( "I presume that the 6 at the very end of the problem is to be an exponent so that the <BR>\n" );
document.write( "problem really is:<BR>\n" );
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document.write( "(X^4Y^8)^1/2*(X^1/2)^6<BR>\n" );
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document.write( "The exponent of 1/2 for the first (left hand) set of parentheses tells you to take the square<BR>\n" );
document.write( "root of the quantity inside the parentheses.  You can also get this through using the power rule<BR>\n" );
document.write( "for exponents and it tells you for a problem such as (x^4*y^8)^1/2 to multiply the 1/2 times<BR>\n" );
document.write( "each of the exponents on the factors inside the parentheses.  So you multiply 1/2 times 4<BR>\n" );
document.write( "to get an answer of 2 as the exponent of x and you multiply the 1/2 times 8 to get 4 as<BR>\n" );
document.write( "the exponent of y.  The result is that you can replace (x^4*y^8)^1/2 by (x^2*y^4).<BR>\n" );
document.write( "When you make that replacement, the problem is reduced to:<BR>\n" );
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document.write( "(x^2*y^4)*(x^1/2)^6<BR>\n" );
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document.write( "Next you can apply the same power rule to the last factor of (x^1/2)^6. To apply this rule<BR>\n" );
document.write( "simply multiply 6 times the exponent inside the parentheses.  The product of 6 times 1/2<BR>\n" );
document.write( "is 3 which then becomes the exponent of x to make the term (x^1/2)^6 equivalent to x^3. So<BR>\n" );
document.write( "make this substitution in the reduced form of the problem and the new reduced form becomes:<BR>\n" );
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document.write( "(x^2*y^4)*(x^3)<BR>\n" );
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document.write( "You can then multiply x^2 by x^3 to get x^5 (add the exponents) and the final answer is<BR>\n" );
document.write( "then x^5*y^4.<BR>\n" );
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document.write( "Hope this shows you how to do problems of this sort through using the power rule for exponents<BR>\n" );
document.write( "and the rule for multiplying two like quantities by adding their exponents.<BR>\n" );
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