document.write( "Question 273496: ((a^2)(b)/9th root((a^3)(b^6))\r
\n" ); document.write( "\n" ); document.write( "can you help me solve this problem please.
\n" ); document.write( "Thanks \n" ); document.write( "

Algebra.Com's Answer #200223 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%28%28a%5E2%29%28b%29%29%2Froot%289%2C+a%5E3b%5E6%29\"$
\n" ); document.write( "In simplifying expressions like this, it is often helpful to replace radicals with fractional exponents. So this is where we'll start:
\n" ); document.write( " $\"%28%28a%5E2%29%28b%29%29%2F%28a%5E3b%5E6%29%5E%281%2F9%29\"$
\n" ); document.write( "Now we can start using our rules and properties of exponents. In the denominator we can use the property, $\"%28pq%29%5Ez+=+p%5Ez%2Aq%5Ez\"$ :
\n" ); document.write( " $\"%28%28a%5E2%29%28b%29%29%2F%28%28a%5E3%29%5E%281%2F9%29%28b%5E6%29%5E%281%2F9%29%29\"$
\n" ); document.write( "Then we can use the power of a power rule (i.e. multiply the exponents):
\n" ); document.write( " $\"%28%28a%5E2%29%28b%29%29%2F%28a%5E%283%2F9%29b%5E%286%2F9%29%29\"$
\n" ); document.write( "Reducing the fractions we get:
\n" ); document.write( " $\"%28%28a%5E2%29%28b%29%29%2F%28a%5E%281%2F3%29b%5E%282%2F3%29%29\"$
\n" ); document.write( "Now we'll use the rule for exponents when dividing (i.e. subtract the exponents):
\n" ); document.write( " $\"a%5E%282-1%2F3%29b%5E%281-2%2F3%29\"$
\n" ); document.write( "To subtract the exponents we need the same denominators:
\n" ); document.write( " $\"a%5E%286%2F3-1%2F3%29b%5E%283%2F3-2%2F3%29\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"a%5E%285%2F3%29b%5E%281%2F3%29\"$
\n" ); document.write( "which may be an acceptable answer. But we could also do the following:
\n" ); document.write( " $\"%28a%5E5%2Ab%29%5E%281%2F3%29\"$
\n" ); document.write( " $\"root%283%2C+a%5E5b%29\"$
\n" ); document.write( " $\"root%283%2C+a%5E3%2Aa%5E2b%29\"$
\n" ); document.write( " $\"root%283%2C+a%5E3%29%2Aroot%283%2C+a%5E2b%29\"$
\n" ); document.write( " $\"a%2Aroot%283%2C+a%5E2b%29\"$ \r
\n" ); document.write( "
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