How do you simplify #((x^-3)^4x^4)/(2x^-3)# and write it using only positive exponents?

2 Answers
Feb 5, 2017

Answer:

See the entire simplification process below:

Explanation:

First, use the rule of exponents to simplify the term in parenthesis in the numerator: #(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#((x^color(red)(-3))^color(blue)(4)x^4)/(2x^-3) -> (x^(color(red)(-3) xx color(blue)(4))x^4)/(2x^-3) -> (x^-12x^4)/(2x^-3)#

Next, use this rule for exponents to simplify the numerator:

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

#(x^color(red)(-12) x^color(blue)(4))/(2x^-3) -> x^(color(red)(-12) +color(blue)(4))/(2x^-3) -> x^-8/(2x^-3)#

Now, use this rule of exponents to complete the simplification using only positive exponents: #x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#

#x^color(red)(-8)/(2x^color(blue)(-3)) -> 1/(2x^(color(blue)(-3)-color(red)(-8))) -> 1/(2x^(color(blue)(-3)+color(red)(8))) -> 1/(2x^5)#

Feb 5, 2017

Answer:

#1/(2x^5)#

Explanation:

# ((x^-3)^4 x^4)/(2x^-3) = (x^-12*x^4)/(2x^-3) = x^-8/(2x^-3) =(x^-5*cancel(x^-3))/ (2*cancel(x^-3))=x^-5/2=1/(2x^5)# [Ans]