Question

Simplify: 100m¹2n4, m >= 0 n >= 0
a)m ^ 3 * n * sqrt(10) m >= 0 n >= 0
b)25m³ n, m >= 0 n >= 0
c)100m2 n, m >= 0 n >= 0
d)100m³n, m >= 0 n >= 0

Answer 1

To simplify the expression \( 100m^{1}n^{4} \), we can start by analyzing it directly in terms of its components:

Given:
\[ 100m^{1}n^{4} = 100 \cdot m^{1} \cdot n^{4} \]

1. We know that \( 100 = 10^2 \), thus we can express it as:
\[ 100 = 10^{2} \]

2. The expression remains unchanged since \( m \) is raised to the first power and \( n \) is raised to the fourth power.

There is no need for root or any complex factorization unless stated in the problem. Therefore, let’s explore the options:

a) \( m^{3} n \sqrt{10} \)
- Not correct, because there are no terms or operations that would produce this structure.

b) \( 25m^{3} n \)
- Not correct, because the coefficients and powers don't match the original expression.

c) \( 100m^{2} n \)
- Not correct, because the powers of both \( m \) and \( n \) do not match the original expression.

d) \( 100m^{3} n \)
- Not correct, again because the powers of \( m \) and \( n \) do not match.

So, reviewing the original expression:
None of the given options simplify \( 100m^{1}n^{4} \) into a correct format. Therefore, it seems like the right simplification hasn’t been presented in any of the options provided.

The simplest form of the expression remains:
\[ 100m^{1}n^{4} \]

If you're looking for a specific way to express it or reduce further, please clarify!