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

Step-by-step 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