Question

What is 4s over 3t to the negative 2nd power times 2s over 6t to the 2nd power? The format is a bit weird .

`((4s)/(3t))^(-2) xx ((2s)/(6t))^2`

Answer 1

`1/16`

Explanation:

`((4s)/(3t))^(-2)*((2s)/(6t))^2`

First when given a negative exponent, I reciprocate the expression and make the exponent positive, so:

`((3t)/(4s))^(2)*((2s)/(6t))^2`

`(3t)^2/(4s)^2*(2s)^2/(6t)^2`

`((3t)(3t))/((4s)(4s))*((2s)(2s))/((6t)(6t))`

`(9t^2)/(16s^2)*(4s^2)/(36t^2)`

Cross simplify:

`(cancel(9t^2))/(cancel(16s^2)4)*(cancel(4s^2))/(cancel(36t^2)4)=`

`1/16`