wait...so you were talking about this question: (c^2/3d^-1)^-2
I thought you were talking about this question:
(2m^4n/3m^-1n^3)^-2
so is my answer to this question (2m^4n/3m^-1n^3)^-2 correct?
Apologies for the confusion. Let's clarify the question and work through it together.
The question you provided is: (2m^4n/3m^-1n^3)^-2
To solve it, we can follow these steps:
Step 1: Simplify the expression inside the parentheses.
Inside the parentheses, we have a fraction where the numerator is 2m^4n and the denominator is 3m^-1n^3.
For the numerator:
- We can combine the like terms, m^4 and n, by adding their exponents. So, 2m^4n remains the same.
For the denominator:
- When we divide two terms with the same base, we subtract the exponents. In this case, we have m^-1 in the denominator, which means we can rewrite it as 1/m^1. So, using the exponent rule, we have 3 * 1/m^1 * n^3.
Simplifying further, we get: 2m^4n / (3 * 1/m * n^3)
Step 2: Simplify the expression outside the parentheses.
The expression outside the parentheses is -2, indicating that we need to apply the exponent to the entire fraction inside.
When we raise a fraction to a negative exponent, we can flip the numerator and denominator and change the sign of the exponent. So, we can rewrite the expression as:
(3 * 1/m * n^3/2m^4n)^2
Step 3: Evaluate the expression.
Now, we can simplify the expression further by squaring each term inside the parentheses:
(9 * 1/m^2 * n^6/4m^8n^2)
We can now multiply the coefficients and combine the like terms:
9/4 * (1/m^2n^-2) * (n^6m^-8)
To multiply the coefficients, we get 9/4. For the variables, we need to combine their exponents:
1/m^2n^-2 can be rewritten as 1/(m^2n^2).
So, our final answer is:
9/4 * 1/(m^2n^2) * n^6m^-8
Which can also be written as:
(9n^6)/(4m^2n^2m^8)
Simplifying further, we have:
(9n^4)/(4m^10)
Therefore, the correct answer to the question (2m^4n/3m^-1n^3)^-2 is (9n^4)/(4m^10).