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

1 Answer
Nov 24, 2016

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

Explanation:

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)#