document.write( "Question 83822: How would I evaluate an expression with a mixed-number exponent, such as 8 to the one and one-third power? \n" ); document.write( "

Algebra.Com's Answer #60297 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
There are two ways. 1 1/3 is actually 1 + 1/3, so you'd have
\n" ); document.write( " $\"8%5E%281%2B%281%2F3%29%29\"$
\n" ); document.write( "Use the rule $\"x%5E%28a%2Bb%29+=+%28x%5Ea%29%28x%5Eb%29\"$
\n" ); document.write( " $\"8%5E%281%2B%281%2F3%29%29+=+%288%5E1%29%288%5E%281%2F3%29%29\"$
\n" ); document.write( "The cube root of 8 is 2
\n" ); document.write( " $\"8%5E%281%2B%281%2F3%29%29+=+8%2A2\"$
\n" ); document.write( " $\"8%2A2+=+16\"$ answer
\n" ); document.write( "The other way is 1 1/3 = 4/3
\n" ); document.write( " $\"8%5E%281%2B%281%2F3%29%29+=+8%5E%284%2F3%29\"$
\n" ); document.write( "Note that 4/3 is actually $\"4%2A%281%2F3%29\"$
\n" ); document.write( "Use the rule $\"x%5E%28a%2Ab%29+=+%28x%5Ea%29%5Eb\"$
\n" ); document.write( " $\"8%5E%284%2F3%29+=+%288%5E%281%2F3%29%29%5E4\"$
\n" ); document.write( " $\"8%5E%284%2F3%29+=+2%5E4\"$
\n" ); document.write( " $\"8%5E%284%2F3%29+=+16\"$ same answer \n" ); document.write( "

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