Question

Assume all variables represent non negative numbers . Help please!!

Answer 1

A).
`2p^(8)`

B).
`3m^(7)`

Explanation:

A).
`\sqrt{4p^(16)}`

To get the square root of the given expression we will convert it into the square form.

`4p^(16)=(2)^2(p^(8))^2` [Since 2×2 = 4 and
`p^(8)* p^(8)=p^(16)`]

Therefore,
`\sqrt{4p^(16)}=\sqrt{2^(2)* (p^(8))^2 }`

`=2p^(8)`

B).
`\sqrt{9m^(44)}`

Since,
`9m^(14)=(3)^2* (m^7)^2`

Therefore,
`\sqrt{9m^(44)}=√((3)^2* (m^7)^2)` [Since 3² = 9 and (m⁷)² = m¹⁴]

`=3m^(7)`