document.write( "Question 1112786: Hi,
\n" ); document.write( "Please help me to solve step-by-step on these questions.
\n" ); document.write( "Thank you very much.\r
\n" ); document.write( "\n" ); document.write( "10. Explain in words how to determine whether :
\n" ); document.write( "
\n" ); document.write( " nth root of a^n = a
\n" ); document.write( " Or
\n" ); document.write( " nth root of a^n = /a/
\n" ); document.write( " Simplify the following expression by first rewriting to remove the negative exponent, then writing in radical form, then evaluating, and final simplifying. Refer to Section 8.2 in the text.
\n" ); document.write( " (-27)/64)^(-2/3)
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #727806 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
It depends on what you know about \"a\" and \"n\".
\n" ); document.write( "If you are given values for \"a\" and \"n\" it is easy:
\n" ); document.write( "
\n" ); document.write( "If \"a%3E=0\" and \"n\" is a positive integer, \"root%28n%2Ca%5En%29=a\" .
\n" ); document.write( "Example #1: for \"a=2\" and \"n=7\" , \"root%287%2C2%5E7%29=root%287%2C128%29=2\" .
\n" ); document.write( "Example #2: for \"a=3\" and \"n=4\" , \"root%286%2C3%5E4%29=root%284%2C81%29=3\" .
\n" ); document.write( "
\n" ); document.write( "If \"a%3C0\" and \"n\" is an even (positive) integer, \"root%28n%2Ca%5En%29=abs%28a%29\" .
\n" ); document.write( "Example #3: for \"a=-5\" and \"n=4\" , \"root%284%2C%28-5%29%5E4%29=root%284%2C625%29=5\" .
\n" ); document.write( "
\n" ); document.write( "If \"a%3C0\" and \"n\" is an odd (positive) integer, \"root%28n%2Ca%5En%29=a\" .
\n" ); document.write( "Example #3: for \"a=-5\" and \"n=3\" , \"root%283%2C%28-5%29%5E3%29=root%284%2C-125%29=-5\" .
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "IF YOU DO NOT HAVE ENOUGH INFORMATION:
\n" ); document.write( "If \"n\" is an even (positive) integer, \"root%28n%2Ca%5En%29=abs%28a%29\" is always true.
\n" ); document.write( "\"root%284%2C%28-5%29%5E4%29=root%284%2C625%29=5=abs%28-5%29\" and \"root%284%2C5%5E4%29=root%284%2C625%29=5=abs%28-5%29\" .
\n" ); document.write( "
\n" ); document.write( "If \"n\" is an odd (positive) integer, \"root%28n%2Ca%5En%29=a\" is always true.
\n" ); document.write( "\"root%283%2C%28-5%29%5E43%29=root%284%2C-125%29=-5\" and \"root%283%2C5%5E3%29=root%284%2C125%29=5\" .
\n" ); document.write( "
\n" ); document.write( "By definition of negative exponent, \"a%5E%28-%222+%2F+3%22%29\"\"%22=%22\"\"1%2Fa%5E%222+%2F+3%22\" ,
\n" ); document.write( "and \"1%2F%22-27+%2F+64%22\"\"%22=%22\"\"-1%2F%2227+%2F+64%22\"\"%22=%22\"\"%28-1%29%2864%2F27%29\"\"%22=%22\"\"-64%2F27\" as you already knew.
\n" ); document.write( "You probably would just write as one step: \"1%2F%22-27+%2F+64%22\"\"%22=%22\"\"-64%2F27\" .
\n" ); document.write( "
\n" ); document.write( "Putting that old and new knowledge together, what you are probably expected to write is
\n" ); document.write( "\"%28-27%2F64%29%5E%22-+2+%2F+3%22\"\"%22=%22\"\"%28-64%2F27%29%5E%222+%2F+3%22\"\"%22=%22\"\"%28root%283%2C-64%2F27%29%29%5E2%29\"\"%22=%22\"\"%28-4%2F3%29%5E2\"\"%22=%22\"\"%2816%2F9%29\" \n" ); document.write( "
\n" );