Question

How do you simplify `(a^7b^5c^8)/(a^5bc^7)`?

Answer 1

See a solution process below:

Explanation:

First, use this rule of exponents to rewrite the `b` denominator:

`a = a^color(red)(1)`

`(a^7b^5c^8)/(a^5b^color(red)(1)c^7)`

Next, use this rule of exponents to eliminate the denominators:

`x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))`

`(a^color(red)(7)b^color(red)(5)c^color(red)(8))/(a^color(blue)(5)b^color(blue)(1)c^color(blue)(7)) = a^(color(red)(7)-color(blue)(5))b^(color(red)(5)-color(blue)(1))c^(color(red)(8)-color(blue)(7)) = a^2b^4c^1`

Now, use this rule of exponents to simplify the `c` term:

`a^color(red)(1) = a`

`a^2b^4c`