Question

How do you simplify `(2a^2b^-7c^10)/(6a^-5b^2c^-3)`?

Answer 1

There are two forms, no fraction, or no negative exponents: `frac{2a^2b^{-7}c^{10}}{6a^{-5} b^2 c^{-3}}` `= 2/6 a^{2 - -5}b^{-7 -2} c^{10 - -3}` `= 3^{-1} a^7b^{-9}c^{13}` `= \frac{a^7c^{13}}{3b^{9}}`

Answer 2

`=(a^7c^13)/(3b^9)`

Explanation:

Recall the law of indices: `x^-m = 1/x^m`

You can get rid of all the negative indices,

`(cancel2a^2color(blue)(b^-7)c^10)/(cancel6^3color(red)(a^-5)b^2color(purple)(c^-3))`

`= (a^2color(red)(a^5)c^10color(purple)(c^3))/(3b^2color(blue)(b^7))`Now simplify by adding the indices of like bases:

`=(a^7c^13)/(3b^9)`