To determine which equation is true among the given options, let's analyze each one step-by-step:
Option A: [tex]\(4 \times n \times n \times n \times n = 4 n^4\)[/tex]
- Here, on the left-hand side, we have [tex]\(4 \times n \times n \times n \times n\)[/tex], which is equivalent to [tex]\(4n^4\)[/tex]. Clearly, this simplifies directly to the right-hand side, [tex]\(4n^4\)[/tex].
- Therefore, [tex]\(4 \times n \times n \times n \times n = 4n^4\)[/tex] is true.
Option B: [tex]\(10 h - 10 = 10 - 10 h\)[/tex]
- Let's simplify the left-hand side first: [tex]\(10h - 10\)[/tex].
- Now, compare it to the right-hand side: [tex]\(10 - 10h\)[/tex].
- These two expressions are not the same; they are actually negatives of each other unless [tex]\(h = 1\)[/tex].
- Therefore, [tex]\(10 h - 10 = 10 - 10h\)[/tex] is generally not true for all [tex]\(h\)[/tex].
Option C: [tex]\(x^2 + 3 v = (x + x) + v \times v \times v\)[/tex]
- The left-hand side is [tex]\(x^2 + 3v\)[/tex].
- The right-hand side is [tex]\((x + x) + v^3\)[/tex] which simplifies to [tex]\(2x + v^3\)[/tex].
- These two expressions are different unless specific values of [tex]\(x\)[/tex] and [tex]\(v\)[/tex] make the equation true by coincidence.
- Therefore, [tex]\(x^2 + 3v \neq 2x + v^3\)[/tex] in general.
Option D: [tex]\(6 \times (2 + 7) = (6 \times 2) + 7\)[/tex]
- Simplify inside the parentheses on the left-hand side: [tex]\(6 \times 9 = 54\)[/tex].
- Now, simplify the right-hand side: [tex]\(6 \times 2 + 7 = 12 + 7 = 19\)[/tex].
- These are clearly different values.
- Therefore, [tex]\(6 \times (2 + 7) \neq 6 \times 2 + 7\)[/tex].
Based on analyzing each equation step-by-step, the true equation is:
Option A: [tex]\(4 \times n \times n \times n \times n = 4n^4\)[/tex].
