simplify the following expression using only positive exponents X^2 y^8 / (x^6y)^2?

x² y⁸

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(x⁶ y)²

1) Clear the parentheses by raising all the powers on the inside to the power on the outside

You raise a power to a power by multiplying the exponents.

After you have cleared the parentheses, you have this:

x² y⁸

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x¹² y²

2) Cancel factors that appear in common in the top and the bottom.

After you cancel two x's and two y's, you end up with this:

y⁶

----- <-- answer

x¹⁰

Answer

y⁶ / x¹⁰

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

x^2y^8 x (x^6y)^-2

(x^2y^8) x (x^-12y^-2)

(x^(2 - 12)) x (y^(8 - 2))

x^-10 x y^6

so,

y^6 / x^10

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

x^2y^8 * (x^6y)^-2

x^2y^8 * x^-12y^-2

x^(2 - 12) * y^(8 - 2)

x^-10 * y^6

y^6 / x^10