Determine the Correct Sign in 0×(15+3-2)^2/4 ? (5+4+1)^2 -6^2×0

Determine the correct sign

$0\times(15+3-2)^2:2^2~[~?~]~(5+4+1)^2-6^2\times0$

To solve this problem, we'll evaluate each side of the inequality using the order of operations and then compare them:

Left Expression: $0 \times (15 + 3 - 2)^2 : 2^2$

• First, evaluate inside the parentheses: $15 + 3 - 2 = 16$.
• Next, apply the exponent: $16^2 = 256$.
• The expression becomes $0 \times 256 : 2^2$.
• Compute the power of 2: $2^2 = 4$.
• The expression is now $0 \times 256 : 4$.
• Divide: $256 : 4 = 64$.
• Finally, multiply by zero: $0 \times 64 = 0$.

Right Expression: $(5 + 4 + 1)^2 - 6^2 \times 0$

• First, evaluate inside the parentheses: $5 + 4 + 1 = 10$.
• Apply the exponent: $10^2 = 100$.
• Compute the other power: $6^2 = 36$.
• The expression becomes $100 - 36 \times 0$.
• Multiply by zero: $36 \times 0 = 0$.
• Subtract: $100 - 0 = 100$.

Now, comparing the values of the two expressions:

• Left expression equals $0$.
• Right expression equals $100$.

Since $0 \ne 100$, the correct sign to use is $\ne$.

Therefore, the solution to the problem is $\ne$.