Question

If x2=y3, what is the value of z does x3z=y9?

Answer 1

If x² = y³ , for what value of z does
`x^(3z)` =
`Y^(9)` ?

Answer:

z= 2

Explanation:

To solve the question given, we will follow the steps below;

`X^(3z)` =
`Y^(9)` -----------------------------------------------------------------(1)

but applying the law of indices mᵃᵇ = (mᵃ)ᵇ

then

`Y^(9)` =
`(Y^(3))^(3)`

replace
`Y^(9)` by
`(Y^(3))^(3)` in equation (1)

`X^(3z)` =
`Y^(9)`

`X^(3z)` =
`(Y^(3))^(3)` --------------------------------------------------------------------(2)

but from the question x² = y³

replace y³ by x² in equation (2)

`X^(3z)` =
`(Y^(3))^(3)`

`X^(3z)` =
`(X^(2))^(3)`

`X^(3z)` =
`X^(6)`

3z = 6

divide both-side of the equation by 3

3z/3 = 6/3

On the left-hand side of the equation, 3 at the numerator will cancel-out 3 at the denominator leaving us with just z while on the right-hand side of the equation 6 will be divided by 3

z= 2