document.write( "Question 43752: what expression raised to the fourth power is\r
\n" ); document.write( "\n" ); document.write( "81x^12y^8z^16 \n" ); document.write( "
Algebra.Com's Answer #28712 by mbarugel(146)\"\" \"About 
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\n" ); document.write( "Notice that your expression is the product of many \"smaller\" expressions:
\n" ); document.write( "81, x^12, y^8 and z^16\r
\n" ); document.write( "\n" ); document.write( "Therefore, in order to find what expression raised to the fourth power yields 81x^12y^8z^16, we can do this for each of the smaller expressions.\r
\n" ); document.write( "\n" ); document.write( "- 81: this is 3 to the 4th power. So we have: 81 = 3^4\r
\n" ); document.write( "\n" ); document.write( "- x^12: This is the same as (x^3)^4. Notice that I'm using the following rule:
\n" ); document.write( "\"%28x%5Ea%29%5Eb+=+x%5E%28a%2Ab%29\"
\n" ); document.write( "So we have: x^12 = (x^3)^4\r
\n" ); document.write( "\n" ); document.write( "- y^8: We use the same rule as above to get y^8 = (y^2)^4\r
\n" ); document.write( "\n" ); document.write( "- z^16: Once again, we use the same rule, getting z^16 = (z^4)^4\r
\n" ); document.write( "\n" ); document.write( "Up to now, we've found that\r
\n" ); document.write( "\n" ); document.write( "81x^12y^8z^16 = 3^4*(x^3)^4*(y^2)^4*(z^4)^4\r
\n" ); document.write( "\n" ); document.write( "So now we use the rule:
\n" ); document.write( "\"%28x%5En%29%28y%5En%29=%28x%2Ay%29%5En\"\r
\n" ); document.write( "\n" ); document.write( "Applying that rule, we conclude that:\r
\n" ); document.write( "\n" ); document.write( "3^4*(x^3)^4*(y^2)^4*(z^4)^4 = ( 3(x^3)(y^2)(z^4) )^4\r
\n" ); document.write( "\n" ); document.write( "Therefore, we've found that 3(x^3)(y^2)(z^4) to the 4th power is equal to your expression.\r
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\n" ); document.write( "\n" ); document.write( "I hope this helps!
\n" ); document.write( "Get more answers at Online Math Answers.com!
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