Respuesta :

gmany

Answer:

[tex]\large\boxed{\dfrac{(x^6y^8)^3}{x^2y^2}=x^{16}y^{22}}[/tex]

Step-by-step explanation:

[tex]\dfrac{(x^6y^8)^3}{x^2y^2}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=\dfrac{(x^6)^3(y^8)^3}{x^2y^2}=\dfrac{x^{(6)(3)}y^{(8)(3)}}{x^2y^2}=\dfrac{x^{18}y^{24}}{x^2y^2}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=x^{18-2}y^{24-2}=x^{16}y^{22}[/tex]

JeanaShupp

Answer: [tex]x^{16}\ y^{22}[/tex]

Step-by-step explanation:

The given expression : [tex]\dfrac{(x^6y^8)^3}{x^2y^2}[/tex]

Using identity , [tex](a^m)^n=a^{mn}[/tex] , we have

[tex]{(x^6y^8)^3=x^{6\times3}\ y^{8\times3}\\\\=x^{18}\ y^{24}[/tex]

Now, [tex]\dfrac{(x^6y^8)^3}{x^2y^2}=\dfrac{x^{18}\ y^{24}}{x^2\ y^2}[/tex]

( its also an equivalent expression to given expression.)

Using identity , [tex]\dfrac{a^n}{a^m}=a^{n-m}[/tex] , we have

[tex]\dfrac{x^{18}\ y^{24}}{x^2\ y^2}=x^{18-2}\ y^{24-2}\\\\=x^{16}\ y^{22}[/tex]

Hence, the expression is equivalent to given expression :

[tex]x^{16}\ y^{22}[/tex]

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