Question

Which expression is equivalent to 64y18 – 1000z6?

(4y6)3 – (10z2)3
(16y6)3 – (10z2)3
(16y6)3 – (100z2)3
(4y6)3 – (100z2)3

Answer 1

`(4y^6)^3 - (10z^2)^3`

Explanation:

Given:
`64y^(18)- 1000z^6`

Solution:

Option 1)
`(4y^6)^3 - (10z^2)^3`

`64y^(18) - 1000z^6`

So, Option 1 is equivalent to
`64y^(18)- 1000z^6`

Option 2)
`(16y^6)^3 -(10z^2)^3`

`4096y^(18) -1000z^6`

So, Option 2 is not equivalent to
`64y^(18)- 1000z^6`

Option 3)
`(16y^6)^3 -(100z^2)^3`

`4096y^(18) -1000000z^6`

So, Option 3 is not equivalent to
`64y^(18)- 1000z^6`

Option 4)
`(4y^6)^3 -(100z^2)^3`

`64y^(18) -1000000z^6`

So, Option 4 is not equivalent to
`64y^(18)- 1000z^6`

Hence
`(4y^6)^3 - (10z^2)^3` is equivalent to
`64y^(18)- 1000z^6`

So, Option A is correct.