Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents. (4a*2)(4a*−1)*2(8b*3)(5b*−1)
To simplify the given expression, we can apply the properties of exponents.
First, let's simplify the numerical portion: (4 * 2) * 2 * (8 * 5) = 16 * 2 * 40 = 1280.
Now, let's simplify the variables with positive exponents:
a^2 * a^(-1) = a^(2 + (-1)) = a^1 = a^1 = a,
and
b^3 * b^(-1) = b^(3 + (-1)) = b^2.
Therefore, the simplified expression is: 1280a(b^2).