Question

How do you simplify `(2a^4b^3 )/(a^2b)`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`2(a^4/a^2)(b^3/b)`

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

`x = x^color(blue)(1)`

`2(a^4/a^2)(b^3/b^color(blue)(1))`

Now, use this rule of exponents to simplify the `a` and `b` terms:

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

`2(a^color(red)(4)/a^color(blue)(2))(b^color(red)(3)/b^color(blue)(1)) =>`

`2a^(color(red)(4)-color(blue)(2))b^(color(red)(3)-color(blue)(1)) =>`

`2a^2b^2`

Answer 2

`2a^2b^2`

Explanation:

Remember that exponents underneath the fraction are the same as negative exponents above the fraction. So this expression is the same as `2a^4b^3a^(-2)b^(-1)`, which one then adds as normal:
`2a^(4-2)b^(3-1)=2a^2b^2`.