How do you simplify #(n^2 times n^3) /n^4#?

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Answer 1 · 2016-12-24T15:34:00

#n#

First, we can simplify the numerator using the rule for exponents which states:

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

#(n^color(red)(2) xx n^color(blue)(3))/n^4 = n^(color(red)(2) + color(blue)(3))/n^4 = n^5/n^4#

Now, we can use another rule for exponents to simplify even further:

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

#(n^color(red)(5))/(n^color(blue)(4)) = x^(color(red)(5) - color(blue)(4)) = n^1#

Finally, we can use one last rule for exponents to complete the simplification of this expression:

#color(red)(x^1 = x)#

#n^1 = n#