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

2 Answers
Dean R.
Apr 19, 2018

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}}

EZ as pi
Apr 22, 2018

=(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)

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