Question

Evaluate without using a calculator (x2y-3)0+x1/3-(4x)1/2 when x = 64 and y = 27. Show work.

Answer 1

Given:

The expression is:

`(x^2y-3)^0+x^{(1)/(3)}-(4x)^{(1)/(2)}`

To find:

The value of the given expression when
`x=64` and
`y=27`.

Solution:

We have,

`(x^2y-3)^0+x^{(1)/(3)}-(4x)^{(1)/(2)}`

Putting
`x=64` and
`y=27`, we get

`=((64)^2(27)-3)^0+(64)^{(1)/(3)}-(4(64))^{(1)/(2)}`

It can be written as

`=((64)^2(27)-3)^0+(4^3)^{(1)/(3)}-(4)^{(1)/(2)}(64)^{(1)/(2)}`

`=1+4-2(8)`
`[\because a^0=1,a\\eq 0]`

`=5-16`

`=-11`

Therefore, the value of the given expression
`-11` when
`x=64` and
`y=27`.