Question

How do you rewrite the expression `(–2x^5)^5(4x^5)^-1` with positive exponents?

Answer 1

The answer is: `-8x^20`.

Using the properties of the powers:

`(-2x^5)^5(4x^5)^-1=(-2)^5(x^5)^5(2^2)^-1(x^5)^-1=-2^5x^25*2^-2x^-5=-2^(5-2)x^(25-5)=-2^3x^20=-8x^20`.

The properties used are:

`a^n*a^m=a^(n+m)`, and

`(a^n)^m=a^(n*m)`.