How do you simplify ${(- r^{5} s)}^{2} {(- r^{2} s^{4})}^{4}$ $(-r^5s)^2(-r^2s^4)^4$ ?

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Answer 1 · 2017-08-07T18:41:44

$r^{18} s^{18}$ $r^18s^18$

Remove the brackets first: multiply the indices.

Raising a negative value to an even power makes it positive:

${(- r^{5} s)}^{2} {(- r^{2} s^{4})}^{4}$ $(-r^5s)^2(-r^2s^4)^4$

$= (+ r^{10} s^{2}) \times (+ r^{8} s^{16})$ $=(+r^10s^2) xx (+r^8s^16)$

$r^{18} s^{18} \leftarrow$ $r^18s^18" "larr$ add the indices of like bases

How do you simplify (−r5s)2(−r2s4)4 (-r^5s)^2(-r^2s^4)^4?