How do you simplify #(\frac { 6x ^ { 6} y ^ { 2} z ^ { 5} } { 3x ^ { 2} y ^ { 1} z ^ { 0} } ) ^ { 3}#?

1 Answer
smendyka
Jul 20, 2017

See a solution process below:

Explanation:

First, use this rule of exponents to simplify the term with in the parenthesis:

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

#((6x^color(red)(6)y^color(red)(2)z^color(red)(5))/(3x^color(blue)(2)y^color(blue)(1)z^color(blue)(0)))^3 => (2x^(color(red)(6)-color(blue)(2))y^(color(red)(2)-color(blue)(1))z^(color(red)(5)-color(blue)(0)))^3 =>#

#(2^1x^4y^1z^5)^3#

Now, use this rule of exponents to complete the simplification:

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

#(2^color(red)(1)x^color(red)(4)y^color(red)(1)z^color(red)(5))^color(blue)(3) => 2^(color(red)(1)xxcolor(blue)(3))x^(color(red)(4)xxcolor(blue)(3))y^(color(red)(1)xxcolor(blue)(3))z^(color(red)(5)xxcolor(blue)(3)) => 2^3x^12y^3z^15 =>#

#8x^12y^3z^15#

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