document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=554487>Question 554487</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me out with this one, \"In this exercise, solve the equation containing a rational exponent on the variable.\"\r<BR>\n" );
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document.write( "x^3/4= 125 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #361356 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=361356\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given to solve for x:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%283%2F4%29+=+125 ALIGN=MIDDLE  ALT=\"x%5E%283%2F4%29+=+125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "One way to solve this is to make use of the power rule of exponents. This rule says:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5Ea%29%5Eb+=+x%5E%28a%2Ab%29 ALIGN=MIDDLE  ALT=\"%28x%5Ea%29%5Eb+=+x%5E%28a%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Or in words ... if you have a base quantity with an exponent, and you raise it to a power, it is equal to the base quantity raised to product of the two exponents.<BR>\n" );
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document.write( "So what would happen if we raised <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%283%2F4%29 ALIGN=MIDDLE  ALT=\"x%5E%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > power. It would be equal to raising x to the exponent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F4%29%2A%284%2F3%29 ALIGN=MIDDLE  ALT=\"%283%2F4%29%2A%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. But in multiplying the two exponents you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F12+=+1 ALIGN=MIDDLE  ALT=\"12%2F12+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So raising <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%283%2F4%29 ALIGN=MIDDLE  ALT=\"x%5E%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > power, it just becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E1 ALIGN=MIDDLE  ALT=\"x%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is just x.<BR>\n" );
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document.write( "However, if you raise one side of this equation to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > power, you must do the same to the other side to maintain the equality. In equation form this is now:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+125%5E%284%2F3%29 ALIGN=MIDDLE  ALT=\"x+=+125%5E%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The product rule means that we can interpret the exponent as the product of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%281%2F3%29 ALIGN=MIDDLE  ALT=\"4%2A%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > The right side of this equation can be interpreted in two ways. Either you can raise 125 to the 4th power and then take the cube root (the exponent 1/3 means cube root) of that answer. Or you can find the cube root (from the 1/3) of 125 and then raise that result to the 4th power.<BR>\n" );
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document.write( "It's easier to do the second method. The cube root of 125 is 5. Then raise that to the 4th power to get 5*5*5*5 = 625. That's the answer to this problem:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+625 ALIGN=MIDDLE  ALT=\"x+=+625\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you in your understanding of exponents.<BR>\n" );
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