Respuesta :
If x² = y³ , for what value of z does [tex]x^{3z}[/tex] = [tex]Y^{9}[/tex] ?
Answer:
z= 2
Step-by-step explanation:
To solve the question given, we will follow the steps below;
[tex]X^{3z}[/tex] = [tex]Y^{9}[/tex] -----------------------------------------------------------------(1)
but applying the law of indices mᵃᵇ = (mᵃ)ᵇ
then
[tex]Y^{9}[/tex] = [tex](Y^{3})^{3}[/tex]
replace [tex]Y^{9}[/tex] by [tex](Y^{3})^{3}[/tex] in equation (1)
[tex]X^{3z}[/tex] = [tex]Y^{9}[/tex]
[tex]X^{3z}[/tex] = [tex](Y^{3})^{3}[/tex] --------------------------------------------------------------------(2)
but from the question x² = y³
replace y³ by x² in equation (2)
[tex]X^{3z}[/tex] = [tex](Y^{3})^{3}[/tex]
[tex]X^{3z}[/tex] = [tex](X^{2})^{3}[/tex]
[tex]X^{3z}[/tex] = [tex]X^{6}[/tex]
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
