Question

What is `(4s^-3t^-4)/(8s^6t^8)`?

Answer 1

I found: `1/(2s^9t^12)`

Explanation:

In this case you can remember a property of division between powers with the same base that tells us:
`a^m/a^n=a^(m-n)`

so that basically if you have a fraction between two exponents with the same base we can write, as result, that base and the difference of the exponents!

in our case we have:

`4/8*s^-3/s^6*t^-4/t^8=`

so we operate with the numbers, the `s` and then the `t`:

`=1/2*s^(-3-6)*t^(-4-8)=1/2*s^(-9)t^(-12)=`

We can now remember another property concerning the sign of the exponent: we can change the sign of the exponent provided that we send the number (with the new exponent) to the "basement" (at the denominator):
for example you can write: `a^-3=1/a^3`
we get:
`=1/2(1/s^9)(1/t^12)=1/(2s^9t^12)`