How do you simplify and write #(-r^4s)^2 (-r^2s^5)^5# with positive exponents?

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Answer 1 · 2017-01-14T18:10:22

#=-r^18s^27#

To simplify you need to get rid of the brackets first:

#color(blue)((-r^4s)^2)color(red)((-r^2s^5)^5)#

Use the law of indices: #(x^m)^n = x^(mn)#

Note that: an odd number of negative signs gives a negative while an even number gives a positive.

#=color(blue)(+r^8s^2) xxcolor(red)(-r^10s^25)#

Now to simplify, use the law of indices....

#x^m xx x^n = x^(m+n)#

#=-r^18s^27#

Note that the negative sign is not the same as a negative index.