Question

Simplify the expression below. Write your answer with only positive exponents.

(a^3b^2c/a^5c^2)(a^2b/c^4)

Answer 1

The expression
`\left((a^3b^2c)/(a^5c^2)\right)\left((a^2b)/(c^4)\right)` is equal to
`(b^3)/(c^5)`

Explanation:

We have the following expression

`\left((a^3b^2c)/(a^5c^2)\right)\left((a^2b)/(c^4)\right)`

To simplify the expression you need to:

The left side of the expression is
`(a^3b^2c)/(a^5c^2)=(b^2)/(a^2c)` because

`\mathrm{Apply\:exponent\:rule}:\quad (x^a)/(x^b)=(1)/(x^(b-a))`

`(a^3)/(a^5)=(1)/(a^(5-3))` and
`(c)/(c^2)=(1)/(c^(2-1))`

`(b^2)/(c^(2-1)a^(5-3)) = (b^2)/(a^2c)`

Next,

`(a^2b)/(c^4)\cdot (b^2)/(a^2c)`

`\mathrm{Multiply\:fractions}:\quad (a)/(b)\cdot (c)/(d)=(a\:\cdot \:c)/(b\:\cdot \:d)`

`(b^2a^2b)/(a^2cc^4)`

`\mathrm{Cancel\:the\:common\:factor:}\:a^2`

`(b^2b)/(cc^4)`

We know that
`b^2b=b^3` and
`cc^4=c^5`

Therefore
`(b^3)/(c^5)`