document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=192974>Question 192974</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with a few problems. I am stuck.\r<BR>\n" );
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document.write( "1) Write the equation (1/5)^-7 = 78125 in logarithmic form.\r<BR>\n" );
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document.write( "2) Simplify the expression  (256x^4y)^1/4/(81xy^3)^3/4  Assume that all variables represent positive numbers\r<BR>\n" );
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document.write( "3) Find the value of x: log 3 27 = x\r<BR>\n" );
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document.write( "4) Assume that all variables are positive and multiply  y^2/6(y^-2/6 + 8y^4/6)\r<BR>\n" );
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document.write( "Any and all help will be appreciated.\r<BR>\n" );
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document.write( "Thanks in advance!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #144840 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=144840\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)(1/5)^-7=78125<BR>\n" );
document.write( "(5/1)^7=78125<BR>\n" );
document.write( "5^7=78125    ok\r<BR>\n" );
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document.write( "log to base  5  of  78125=7\r<BR>\n" );
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document.write( "checklog78126/log5=7  ok\r<BR>\n" );
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document.write( "2) ( (256x^4y)^(1/4))/( (81xy^3)^(3/4))<BR>\n" );
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document.write( "256^.25=4<BR>\n" );
document.write( "(x^4)^.25=x^1=x<BR>\n" );
document.write( "den<BR>\n" );
document.write( "81^(3/4)= (81^.25)^3=3^3=27<BR>\n" );
document.write( "(y^3)^(3/4)=(y^(9/4)<BR>\n" );
document.write( "combining<BR>\n" );
document.write( "( 4*x*y^.25)/ ( 27*x^.75*y^(9/4))<BR>\n" );
document.write( "remember  to  divide common  bases,, subst  exponents<BR>\n" );
document.write( "(4x^.250/(27y^2)\r<BR>\n" );
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document.write( "check,  let  x=2,  y=3<BR>\n" );
document.write( "answer  (4*2^.25)/(27*3^2) =.01957<BR>\n" );
document.write( "original  ((256*2^4*3)^.25)/( ( 81*2*3^3)^.75)<BR>\n" );
document.write( "10.5286/537.85 = .0196  ok\r<BR>\n" );
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document.write( "3)  log  base  3  of  27 = x<BR>\n" );
document.write( "log27/log3=3=x\r<BR>\n" );
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document.write( "check  3^3=27  ok\r<BR>\n" );
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document.write( "4)  (y^(2/6))*(y^(-2/6)+8y^(4/6))<BR>\n" );
document.write( "y^(2/6-2/6) +8 y^(2/6+4/6)<BR>\n" );
document.write( "Y^0 +8y^1<BR>\n" );
document.write( "1+8y </SPAN>\n" );
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