How do you multiply #(n ^ { 4} ) ^ { - 4} \cdot n#?

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Answer 1 · 2017-03-11T15:36:09

See the entire solution process below:

First, consolidate the term on the left using this rule of exponents:

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

#(n^color(red)(4))^color(blue)(-4) * n = n^(color(red)(4) xx color(blue)(-4)) * n = n^-16 * n#

Next, use these rules of exponents to combine the two #n# terms:

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

#n^-16 * n = n^color(red)(-16) * n^color(blue)(1) = x^(color(red)(-16) + color(blue)(1)) = n^-15#

If you want to have only positive exponents you can use this rule of exponents to handle this:

#x^color(red)(a) = 1/x^color(red)(-a)#

#n^color(red)(-15) = 1/n^color(red)(- -15) = 1/n^15#