How do you simplify #(\frac { 2z ^ { 6} w ^ { 4} } { 8z ^ { 5} w ^ { 3} } ) ^ { 3}#?

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Answer 1 · 2017-11-20T16:20:19

See a solution process below:

First, reduce the coefficients to:

#((z^6w^4)/(4z^5w^3))^3#

Next, use this rule for exponents to simplify the variables within the parenthesis:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#((z^color(red)(6)w^color(red)(4))/(4z^color(blue)(5)w^color(blue)(3)))^3 =>#

#((z^(color(red)(6)-color(blue)(5))w^(color(red)(4)-color(blue)(3)))/4)^3 =>#

#((z^color(red)(1)w^color(red)(1))/4)^3#

Then, use this rule of exponents to rewrite the denominator as:

#a = a^color(red)(1)#

#((z^color(red)(1)w^color(red)(1))/4^color(red)(1))^3#

Now, use this rule of exponents to eliminate the outer exponent:

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

#(z^(color(red)(1)xxcolor(blue)(3))w^(color(red)(1)xxcolor(blue)(3)))/4^(color(red)(1)xxcolor(blue)(3) =>#

#(z^3w^3)/4^3 =>#

#(z^3w^3)/64#