Question

How do you simplify `((9p^2q^-1)/(2p^-2))^2 * ((3q^-8)/(4p^-$))^-1`?

Answer 1

`= 27p^4q^6`

Explanation:

`x^-1 = 1/x`
Hope it 4 and not $ in the second term.

Given problem is # ((9p^2q^-1)/(2p^-2)) ^2 * ((3q^-8)/ (4p^-4))^-1#

`= ( (9p^2*p^2)/(2q))^2 * (1/((3q^-8)/(4p^-4)))`
`= ((9^2p^8)/(2^2q^2))*(( 4p^(-4)) / (3q^(-8)))`

`= ((81*p^8)/(4q^2)) * ((4q^8)/(3p^4))`
Removing brackets,

`(81*p^8*4* q^8) / (4q^2*3p^4)=27(p^4q^6)`