How do you condense #(2n ^ { - 2} \cdot n ^ { 4} ) ^ { 4}#?

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Answer 1 · 2017-03-11T15:31:23

See the entire solution process below:

First, use this rule of exponents to combine or condense the terms within the parenthesis:

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

#(2n^color(red)(-2) * n^color(blue)(4))^4 = (2n^(color(red)(-2) + color(blue)(4)))^4 = (2n^2)^4#

Now, we can use these rules for exponents to complete the condensing:

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

#(2n^2)^4 = (2^color(red)(1)n^color(red)(2))^color(blue)(4) = 2^(color(red)(1) xx color(blue)(4))n^(color(red)(2) xx color(blue)(4)) =2^4n^8 = 16n^8#

Answer 2 · 2017-03-11T17:11:56

#16n^8#

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

#:.(a^color(red)m)^color(blue)n=a^(a^(color(red)m xx color(blue)n))#

#:.=2^(1 xx 4)n^(-2 xx 4)*n^(4 xx 4)#

#:.=2^4n^-8*n^16#

#a^color(red)m*m^color(blue)n=a^(color(red)m+color(blue)n)#

#:.=2^4n^(-8+16)#

#:.=2*2*2*2n^8#

#:.=16n^8#