Final answer:
The expression ((2m^(4)n^(2))/(4m^(2)))^(4) simplifies to (m^2n^2)^4 or (m^(2*4))(n^(2*4)), which equals m^8n^8 when expressed with positive exponents.
Step-by-step explanation:
To simplify the given expression, start by simplifying the terms within the parentheses. First, reduce 2m^(4)n^(2) divided by 4m^(2). The 2 and 4 in the numerator and denominator can be divided by 2 to get m^(4)n^(2)/2m^(2). Next, simplify further by canceling out common terms: m^(4-2)n^(2)/2 = m^(2)n^(2)/2. This expression, when raised to the power of 4, becomes ((m^2n^2)/2)^4. To simplify further, apply the exponent to each term inside the parentheses, resulting in (m^(2*4))(n^(2*4)), which simplifies to m^8n^8 when using positive exponents.
When given an expression with multiple terms involving exponents, simplification involves combining like terms and applying exponent rules. In this case, after reducing the fraction within the parentheses and raising it to the fourth power, the exponents inside the parentheses are multiplied by the exponent outside. This process results in m^8n^8 as the final expression using only positive exponents, as all negative exponents are resolved through multiplication by the power outside the parentheses.