Question

How do you simplify `(64qt)/(16q^2t^3)` and find the excluded values?

Answer 1

See a solution process below:

Explanation:

To simplify this expression, first rewrite the expression as:

`64/16(q/q^2)(t/t^3) =>`

`4(q/q^2)(t/t^3)`

Next, use this rule of exponents to rewrite the expression:

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

`4(q^color(red)(1)/q^2)(t^color(red)(1)/t^3)`

Now, use this rule for exponents to simplify the `q` and `t` terms:

`x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))`

`4(q^color(red)(1)/q^color(blue)(2))(t^color(red)(1)/t^color(blue)(3)) =>`

`4(1/q^(color(blue)(2)-color(red)(1)))(1/t^(color(blue)(3)-color(red)(1))) =>`

`4(1/q^1)(1/t^2) =>`

`4(1/q)(1/t^2) =>`

`4/(qt^2)`

To find the exclude values for this expression we need to equate the denominator of the original expression to `0` and solve for each term equal to `0`:

`16q^2t^3 = 0`

First Excluded Value:

`q^2 = 0`

`q = 0`

Second Excluded Value:

`t^3 = 0`

`t = 0`

The Excluded Values Are: `q = 0` and/or `t = 0`