What is the simplified form of
(1/2x^-2)^3 X^7?
To find the simplified form of the expression (1/2x^-2)^3 * x^7, we can follow these steps:
Step 1: Simplify the expression within parentheses.
The expression inside the parentheses is 1/2x^-2. To simplify it, we can apply the following rules:
- When multiplying fractions, we multiply the numerators together and the denominators together.
- When dividing exponents with the same base, we subtract the exponents.
So, 1/2x^-2 can be rewritten as (1/2) * (1/x^2) = 1/(2x^2).
Step 2: Simplify the expression by applying the exponent rule (power rule).
To multiply the same base with exponents, we add the exponents. In this case, we have x^7 * x^(-6).
x^7 * x^(-6) can be rewritten as x^(7+(-6)) = x^1 = x.
Step 3: Multiply the simplified expressions.
We now have 1/(2x^2) * x, which can be written as x/(2x^2).
So, the simplified form of the expression (1/2x^-2)^3 * x^7 is x/(2x^2).