document.write( "Question 40419: Solve this:
\n" ); document.write( "(9x^6*y^8)^(1/6)\r
\n" ); document.write( "\n" ); document.write( "And I have this possible answers\r
\n" ); document.write( "\n" ); document.write( "a. xy(9y8)^(1/6)
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Algebra.Com's Answer #25784 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
Solve this:\r\n" );
document.write( "(9x6y8)1/6\r\n" );
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document.write( "And I have this possible answers\r\n" );
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document.write( "a. xy(9y8)1/6\r\n" );
document.write( "b. xy(3y)1/3 <------- that's the answer!\r\n" );
document.write( "c. 3xy\r\n" );
document.write( "d. x(9y2)1/6\r\n" );
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document.write( "(9x6y8)1/6\r\n" );
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document.write( "Write the 9 as 32 \r\n" );
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document.write( "(32x6y8)1/6\r\n" );
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document.write( "Remove the parentheses by multiplying each inner exponent by the\r\n" );
document.write( "outer exponent 1/6\r\n" );
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document.write( "3(2)(1/6)x(6)(1/6)y(8)(1/6)\r\n" );
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document.write( "32/6x6/6y8/6\r\n" );
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document.write( "Reduce the fraction exponents\r\n" );
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document.write( "31/3x1y4/3\r\n" );
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document.write( "Change improper fraction exponent 4/3 to 1 1/3 but write it as 1+1/3\r\n" );
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document.write( "31/3x1y1+1/3\r\n" );
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document.write( "Now since we add exponents of like bases to multiply, we can use that \r\n" );
document.write( "fact in reverse, and when we see an exponent consisting of an addition,\r\n" );
document.write( "such as in y1+1/3 we can write that as the multiplication y1y1/3.\r\n" );
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document.write( "31/3x1y1y1/3\r\n" );
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document.write( "Now we put the two factors which have the same exponent 1/3 together\r\n" );
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document.write( "31/3y1/3x1y1\r\n" );
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document.write( "Now since to remove parentheses we multiply the inner exponents by the\r\n" );
document.write( "outer exponents, we can use that fact in reverse to say that when two\r\n" );
document.write( "factors have the same exponents, we can put the product of the bases\r\n" );
document.write( "inside parentheses and use the common exponent outside the parentheses,\r\n" );
document.write( "so 31/3y1/3 can be written as (3y)1/3\r\n" );
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document.write( "So the above becomes\r\n" );
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document.write( "(3y)1/3x1y1\r\n" );
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document.write( "We can erase the 1 exponents and get\r\n" );
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document.write( "(3y)1/3xy\r\n" );
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document.write( "which is the same as\r\n" );
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document.write( "xy(3y)1/3\r\n" );
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document.write( "which is answer b.\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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