How do yo simplify #\frac { ( 2a ^ { 6} b ^ { 5} ) ^ { 2} } { ( a ^ { 2} b ^ { 4} ) ^ { 0} \cdot ( 2a b ^ { - 3} ) ^ { 2} }#?

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Answer 1 · 2016-12-08T00:00:56

#a^10b^16#

First, expand each term in parenthesis using the rules for exponents (#color(red)(x^(a^b)=x^(a*b))#) and (#color(red)(x^0 = 1)#):

#(2^2a^(6*2)b^(5*2))/(1*2^2a^(1*2)b^(-3*2))#

#(4a^12b^10)/(4a^2b^-6)#

Now we can divide common terms using another rule for exponents (#color(red)(x^a/x^b = x^(a - b))#):

#(4/4)a^(12-2)b^(10--6)#

#1a^10b^16#

#a^10b^16#