Simplify: 100m¹2n4, m = 0 n = 0

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

GPT-4o mini · Answer

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!