Simplify (x^2y^3)^-2(x^4)^2

Answer 1

To simplify, we can apply the power rule, which states that when raising an exponent to another exponent, we multiply the exponents.

First, let's simplify the expression inside the parenthesis:
(x^2y^3)^-2 = x^(2*-2)y^(3*-2) = x^-4y^-6 = 1/(x^4y^6)

Now, let's simplify the expression outside the parenthesis:
(x^4)^2 = x^(4*2) = x^8

Putting it all together, the simplified expression is:
1/(x^4y^6) * x^8 = x^8 / (x^4y^6) = x^(8-4)y^-6 = x^4y^-6 or 1/(x^(-4)y^6)