im having trouble with simplifying an expression into the form of ax^n. no negative exponents aloud in final answer

Question

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

Answer 1

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.