Question

To evaluate 1254/3 find

a.the square root of 4 times the cube root of 125.
b.125 to the power of 4 and then take the cube root.
c.the fourth root of 125 and then take the cube root.
d.the cube root of 125 and then take the fourth root.

Answer 1

`625`

Explanation:

Given is a number 125 and we have to find out the value when the number is raised to power
`(4)/(3)`

i.e. we have to find the value of
`125^{(4)/(3) }`

This is equivalent to finding cube root of 125 and then raising answer to power 4.

because
`125^{(4)/(3) }=(125^{(1)/(3) })^4\\`

Also since 125 is a perfect cube calculations would be easier

=
`5^4 = 625`

Answer 2

To evaluate


`125^{(4)/(3)`

b. 125 to the power of 4 and then take the cube root.


_____
125^(4/3) = (125^1)×(125^(1/3)) = 125∛125
You can evaluate this more easily by multiplying 125 by its cube root.
125×∛125 = 125×5 = 625