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

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Answer 1 · 2016-11-24T14:43:52

#-(1)/(4b^2a^2)#

First, expand the term in parenthesis using the rules for exponents:

#-(2a^0b^-3 * - a^4b^4)/(-2^3b^3a^(2*3))#

#-(2a^0b^-3 * - a^4b^4)/(-2^3b^3a^6)#

Next, simplify the numerator #a^0 = 1#:

#-(2b^-3* -a^4b^4)/(-2^3b^3a^6)#

Now, multiply the terms in the numerator using the rules for exponents:

#-(-2a^4b^(4-3))/(-2^3b^3a^6)#

#-(-2a^4b^1)/(-2^3b^3a^6)#

Finally, simplify the numerator and denominator using the rules for exponents:

#-(1)/(-2^2b^(3-1)a^(6-4))#

#-(1)/(4b^2a^2)#