How do you simplify #(\frac { x ^ { 4} \cdot x } { x ^ { 2} } ) ^ { 4}#?

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Answer 1 · 2017-05-19T18:57:22

See a solution process below:

First, use these rules of exponents to simplify the numerator within the parenthesis:

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

#((x^4 * x)/x^2)^4 => ((x^color(red)(4) * x^color(blue)(1))/x^2)^4 => (x^(color(red)(4) + color(blue)(1))/x^2)^4 => (x^5/x^2)^4#

Next, use this rule of exponents to simplify the term within the parenthesis:

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

#(x^color(red)(5)/x^color(blue)(2))^4 = (x^(color(red)(5)-color(blue)(2)))^4 => (x^3)^4#

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))#

#(x^color(red)(3))^color(blue)(4) = x^(color(red)(3) xx color(blue)(4)) => x^12#