Question

What's the answer for this question? (The numbers after the letters are indexes btw) 27a9 x 18b5 x 4c2 Over 18a4 x 12b2 x 2c

Answer 1

`(27a^9 * 18b^5 * 4c^2 )/(18a^4 * 12b^2 * 2c) = (9)/(2)a^5b^3c`

Explanation:

Given

`(27a^9 * 18b^5 * 4c^2 )/(18a^4 * 12b^2 * 2c)`

Required

Simplify

`(27a^9 * 18b^5 * 4c^2 )/(18a^4 * 12b^2 * 2c)`

Cancel out 18

`(27a^9 * b^5 * 4c^2 )/(a^4 * 12b^2 * 2c)`

Divide 4 and 2

`(27a^9 * b^5 * 2c^2 )/(a^4 * 12b^2 *c)`

Divide 27 and 12 by 3

`(9a^9 * b^5 * 2c^2 )/(a^4 * 4b^2 *c)`

Apply law of indices

`(9a^(9-4) * b^(5-2) * 2c^(2-1) )/(4)`

`(9a^5 * b^3 * 2c )/(4)`

Divide 2 and 4

`(9a^5 * b^3 * c)/(2)`

`(9a^5b^3c)/(2)`

Rewrite as:

`(9)/(2)a^5b^3c`

Hence:

`(27a^9 * 18b^5 * 4c^2 )/(18a^4 * 12b^2 * 2c) = (9)/(2)a^5b^3c`