Question

Match the numerical expressions to their simplified forms

Answer 1

4

2

3

1

Explanation:

• 
  `$ (a^x)^{(1)/(y)} = a^(x)/(y) $`
• 
  `$ (a^x)/(a^y) = a^(x - y) $`

1)
`(p^6.q^{{(3)/(2)}})^{{(1)/(3)}}`

Therefore,
`$ p^{(6)/(3)}.q^{(3)/(2).(1)/(3)} $`

`$ \implies p^2.q^{(1)/(2)} $`

2)
`$ (p^5)/(p^(-3)q^(-4)) $`

`$ = p^5.p^3.q^4 = p^8.q^4 $`

Now,
`$ (p^8q^4)^{(1)/(4)} $`

`$ \implies p^{(8)/(4)}.q^{(4)/(4)} $`

`$ = p^2. q $`

3)
`$ ((p^2.q^7)/(q^4) )^{(1)/(2) $`

`$ \implies p^{{(2)/(2)}}.q^{(3)/(2)} $`

`$ \implies pq^{(3)/(2)} $`

4)
`$ \frac{(pq^3)^{{(1)/(2)}}}{(pq)^{{(-1)/(2)}}} $`

`$ \implies p^{{(1)/(2)}}q^{{(3)/(2)}}. p^{{(1)/(2)}}.q^{{(1)/(2)}}} $`

`$ = pq^2 $`

Hence, the answers.