Question

Which expression is equivalent to 4 sqrt x^10

Answer 1

`4\sqrt{x^(10)}=4√((x^5)^2)=4|x^5|`

`\text{Used:}\\\\(a^n)^m=a^(n\cdot m)\\\\√(a^2)=|a|`

Answer 2

`4x^(5)`

Explanation:

The given expression is
`4\sqrt{x^(10)}`

We have to simplify the given expression

`4\sqrt{x^(10)}=4\sqrt{(x)^(5)(x)^(5)}`

=
`4\sqrt{(x^(5))^(2)}`

=
`4[(x^(5))^(2)]^{(1)/(2)}`

=
`[(x^(5))^{2* (1)/(2)}]` [Since
`[a^(m)]^(n)=a^(m* n)`

=
`4x^(5)`

Therefore, the expression equivalent to the given expression will be
`4x^(5)`