Question

Which expression is equivalent to (x^6y^8)^3\x^2y^2

Answer 1

`\large\boxed{((x^6y^8)^3)/(x^2y^2)=x^(16)y^(22)}`

Explanation:

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

Answer 2

Answer:
`x^(16)\ y^(22)`

Explanation:

The given expression :
`((x^6y^8)^3)/(x^2y^2)`

Using identity ,
`(a^m)^n=a^(mn)` , we have

`{(x^6y^8)^3=x^(6*3)\ y^(8*3)\\\\=x^(18)\ y^(24)`

Now,
`((x^6y^8)^3)/(x^2y^2)=(x^(18)\ y^(24))/(x^2\ y^2)`

( its also an equivalent expression to given expression.)

Using identity ,
`(a^n)/(a^m)=a^(n-m)` , we have

`(x^(18)\ y^(24))/(x^2\ y^2)=x^(18-2)\ y^(24-2)\\\\=x^(16)\ y^(22)`

Hence, the expression is equivalent to given expression :

`x^(16)\ y^(22)`