Question

How do you simplify `\frac { 7c ^ { - 6} } { 3c ^ { 5} w ^ { - 3} }`?

Answer 1

`(7c^(-6))/(3c^5w^(-3)) = color(orange)((7w^3)/(3c^11))`

Explanation:

Remember that `b^(-e)=1/(b^e)` and `1/(b^(-e))=b^e`

Decomposing `(color(red)7color(green)(c^(-6)))/(color(blue)3color(cyan)(c^5)color(magenta)(w^(-3))`

`color(white)("XXX")=color(red)7 xx color(green)(c^(-6))xxcolor(blue)(1/3)xxcolor(cyan)(1/(c^5))xxcolor(magenta)(1/(w^-3)))`

`color(white)("XXX")=color(red)7 xx color(green)(1/c^6)xxcolor(blue)(1/3)xxcolor(cyan)(1/(c^5))xxcolor(magenta)(w^3)`

`color(white)("XXX")=(color(red)7xxcolor(blue)(1/3)) xx (color(green)(1/c^6)xxcolor(cyan)(1/(c^5)))xx(color(magenta)(w^3))`

`color(white)("XXX")=7/3 xx 1/c^11 xx w^3`

`color(white)("XXX")=(7w^3)/(3c^11)`