How do you simplify #(- 2x ^ { 2} ) ^ { 2} \cdot ( x ^ { 2} ) ^ { - 1}#?

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Answer 1 · 2018-01-09T19:44:51

See a solution process below:

First, we can use these rules for exponents to simplify the two terms in parenthesis:

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

#(-2x^2)^2 * (x^2)^-1 =>#

#(-2^color(red)(1)x^color(red)(2))^color(blue)(2) * (x^color(red)(2))^color(blue)(-1) =>#

#(-2^(color(red)(1)xxcolor(blue)(2))x^(color(red)(2)xxcolor(blue)(2))) * x^(color(red)(2)xxcolor(blue)(-1)) =>#

#(-2^2x^4) * x^-2 =>#

#(4x^4) * x^-2#

Next, we can rewrite this expression as:

#4(x^4 * x^-2)#

Now, we can use this rule for exponents to complete the simplification as:

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

#4(x^color(red)(4) * x^color(blue)(-2)) =>#

#4x^(color(red)(4) + color(blue)(-2)) =>#

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

#4x^2#