How do you evaluate #(2y ^ { 2} \cdot y ^ { 3} \cdot 3y ) ^ { 3}#?

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Answer 1 · 2017-11-14T01:52:31

See a solution process below:

First, rewrite the expression as:

#((2 * 3)(y^2 * y^3 * y))^3 =>#

#(6(y^2 * y^3 * y))^3#

Next, use these rules of exponents to evaluate the #y# terms within the parenthesis:

#a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#(6(y^2 * y^3 * y))^3 =>#

#(6(y^color(red)(2) * y^color(blue)(3) * y^color(purple)(1)))^3 =>#

#(6y^(color(red)(2)+color(blue)(3)+color(purple)(1)))^3 =>#

#(6y^6)^3#

Now, use these rules of exponents to complete the evaluation:

#a = a^color(red)(1)# and #(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#(6y^6)^3 =>#

#(6^color(red)(1)y^color(red)(6))^color(blue)(3) =>#

#6^(color(red)(1) xx color(blue)(3))y^(color(red)(6) xx color(blue)(3)) =>#

#6^3y^18 =>#

#216y^18#