%5E4-%5E3.jpeg "(m^3n^2/2m)^4 ^3")
Simplifying the Expression (m^3n^2/2m)^4^3
This problem involves simplifying an expression with exponents and fractions. Let's break it down step-by-step:
1. Simplifying the Inner Expression
First, we'll simplify the expression inside the parentheses:
- m^3 / m = m^(3-1) = m^2
Now the expression becomes:
(m^2n^2 / 2)^4^3
2. Simplifying the Exponents
We need to deal with the exponents, starting from the innermost:
- 4^3 = 4 * 4 * 4 = 64
The expression now looks like:
(m^2n^2 / 2)^64
3. Applying the Power of a Quotient Rule
The power of a quotient rule states that (a/b)^n = a^n / b^n. Applying this rule, we get:
(m^2n^2)^64 / 2^64
4. Applying the Power of a Product Rule
The power of a product rule states that (ab)^n = a^n * b^n. Applying this rule, we get:
(m^2)^64 * (n^2)^64 / 2^64
5. Simplifying Further
Finally, we simplify by multiplying the exponents:
m^(264) * n^(264) / 2^64
m^128 * n^128 / 2^64
Conclusion
Therefore, the simplified form of the expression (m^3n^2/2m)^4^3 is m^128 * n^128 / 2^64.