Question 187053
{{{(-2a^2*b^3)^2 /(2a^2*b)^3 }}} Start with the given expression.



{{{((-2)^1a^2*b^3)^2 /((2)^1a^2*b^1)^3 }}} Rewrite {{{-2}}} as {{{(-2)^1}}}. Rewrite {{{2}}} as {{{(2)^1}}}. Rewrite {{{b}}} as {{{b^1}}}



{{{((-2)^(1*2)a^(2*2)*b^(3*2)) /((2)^(1*3)a^(2*3)*b^(1*3)) }}} Multiply the outer exponent by EVERY exponent in the parenthesis



{{{((-2)^2a^4*b^6) /((2)^3a^6*b^3) }}} Multiply



{{{(4a^4*b^6) /(8a^6*b^3) }}} Square -2 to get 4. Cube 2 to get 8



{{{(a^4*b^6) /(2a^6*b^3) }}} Reduce {{{4/8}}} to get {{{1/2}}} (these are the coefficients).



{{{(a^(4-6)*b^(6-3)) /(2) }}} Subtract the exponents to divide the monomials.



{{{(a^(-2)*b^3) /(2) }}} Subtract



{{{(b^3) /(2a^2) }}} Flip the variable that has the negative exponent to make the exponent positive.



So {{{(-2a^2*b^3)^2 /(2a^2*b)^3=(b^3) /(2a^2) }}} where {{{a<>0}}} or {{{b<>0}}}