(((40x)^-8)/((-4x)^-2)^4)(((40x)^-8)/((-4x)^-2)^4)

Hi, Julia.

It looks to me like your problem is:

(40x)^{8 } _{•} (40x)^{-8}

(-4x)^{2^4} (-4x)^{-2^4}

When an exponent is raised to another exponent, as in the denominator, you multiply the exponents.

(40x)^{8} _{•} (40x)^{-8}

(-4x)^{8} (-4x)^{-8}

What I see here is the same base in both numerators and the same base in both denominators, so I am going to simplify the exponents further. When the same bases are multiplied, then you add the exponents.

8 + -8 = 0, so:

(40x)^{0}

(-4x)^{0}

Anything to the zero power is 1, so this simplifies to 1/1, or 1.

Hope this helps.