Answer:
[tex]\frac{(x^2y)^2(xy)^3z^2)}{((xy^2)^2yz)}[/tex] = x⁵z
Step-by-step explanation:
Expression given in the question:
[tex]\frac{(x^2y)^2(xy)^3z^2)}{((xy^2)^2yz)}[/tex]
now,
when the power is applied to the number with power, the power of the number gets multiplied i.e
(Xᵃ)ᵇ = Xᵃᵇ
The number having same base when multiplied together, the powers of the numbers gets added
Xᵃ × Xᵇ = Xᵃ⁺ᵇ
and,
The number having same base are when divided , the powers of the numbers gets subtracted
[tex]\frac{X^a}{X^b}[/tex] = Xᵃ⁻ᵇ
thus using the above property, we get
⇒ [tex]\frac{(x^{2}\times2}y^2)(x^3y^3)z^2)}{((x^2y^{2\times2})yz)}[/tex]
or
⇒ [tex]\frac{(x^{4}y^2)(x^3y^3)z^2)}{((x^2y^{4})yz)}[/tex]
or
⇒ [tex]\frac{(x^{4}x^3y^2y^3)z^2)}{(x^2y^{4}yz)}[/tex]
or
⇒ [tex]\frac{(x^{4+3}y^{2+3})z^2)}{(x^2y^{4+1}z)}[/tex]
or
⇒ [tex]\frac{(x^{7}y^{5})z^2)}{(x^2y^{5}z)}[/tex]
or
⇒ [tex](x^{7-2}y^{5-5})z^{2-1})[/tex]
or
⇒ [tex](x^{5}y^{0})z^{1})[/tex]
or
⇒ x⁵z
