Question

(2pm^-1q^0)^-4 • 2m ^-1 p^3 / 2pq^2

Answer 1

`(m^3)/(16p^2q^2)`

Explanation:

Given:

`(2pm^(-1)q^0)^(-4)\cdot ( 2m^(-1) p^3)/(2pq^2)`

1.

`m^(-1)=(1)/(m)`

2.

`q^0=1`

3.

`2pm^(-1)q^0=2p\cdot (1)/(m)\cdot 1=(2p)/(m)`

4.

`(2pm^(-1)q^0)^(-4)=\left((2p)/(m)\right)^(-4)=\left((m)/(2p)\right)^4=(m^4)/((2p)^4)=(m^4)/(16p^4)`

5.

`m^(-1)=(1)/(m)`

6.

`2m^(-1) p^3=2\cdot (1)/(m)\cdot p^3=(2p^3)/(m)`

7.

`( 2m^(-1) p^3)/(2pq^2)=((2p^3)/(m))/(2pq^2)=(2p^3)/(m)\cdot (1)/(2pq^2)=(p^2)/(mq^2)`

8.

`(2pm^(-1)q^0)^(-4)\cdot ( 2m^(-1) p^3)/(2pq^2)=(m^4)/(16p^4)\cdot (p^2)/(mq^2)=(m^3)/(16p^2q^2)`