short answer.Simplify the following expression,and rewrite it in an equivalent form with positive exponents. (-2x^-2)^-4
(-2x^-2)^-4=1/(-2x^-2)^4 = 1 / 16x^-8 =
x^8/16.
To simplify the expression (-2x^-2)^-4 and rewrite it with positive exponents, we can follow these steps:
Step 1: Distribute the exponent -4 to the base (-2x^-2).
(-2x^-2)^-4 = -2^-4 * (x^-2)^-4
Step 2: Simplify each term individually.
For -2^-4, when a negative number is raised to an even power, it becomes positive. So, -2^-4 is equivalent to 1/(-2)^4 or 1/16.
For (x^-2)^-4, we need to apply the power of a power rule by multiplying the exponents. So, x^-2 raised to the power of -4 becomes x^((-2)*(-4)) or x^8.
Step 3: Combine the simplified terms.
Therefore, (-2x^-2)^-4 simplifies to 1/16 * x^8.
In summary, the simplified expression with positive exponents is 1/16 * x^8.