Question

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

Answer 1

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

Explanation:

The given expression is

`((x^6y^8)^3)/(x^2y^2)`

Recall and apply:
`(a^m)^n=a^(mn)` to the numerator to obtain;

`(x^(6* 3)y^(8* 3))/(x^2y^2)`

`(x^(18)y^(24))/(x^2y^2)`

Recall that;
`(a^m)/(a^n)=a^(m-n)`

We apply this property to obtain;

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

Answer 2

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

Explanation:

Given in the question an expression,

`((x^6 y^8)^3)/(x^2 y^2)`

Step 1

The "power rule" tells us that to raise a power to a power, just multiply the exponents.

`(x^(n))^(m) =x^(nm)`

`((x^(6x3)y^(8x3)))/(x^2 y^2)`

`((x^(18)y^(24)))/(x^2 y^2)`

Step 2

The "quotient rule" tells us that we can divide two powers with the same base by subtracting the exponents.

`(x^(n) )/(x^(m))=x^(n-m)`

`(x^(18-2)y^(24-2))`

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