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**Hint:**PEMDAS rule gives the order of operators in the calculation of a mathematical problem. The full form of each initial is P= Parenthesis (brackets); E= Exponents;

M= Multiply; D= Divide; A= Addition; S= Subtraction. We solve inside the brackets, then do exponents, multiply and divide before going for addition and subtraction.

**Complete step-by-step solution:**

As per the given question, we need to simplify \[40+40\cdot 0+1\]. Here, we have three terms separated by addition operator. We need to simplify each term out of these three terms to a single answer. Then we have to add or subtract these single answers based on the operators present.

Using PEMDAS rule, first we check inside the parenthesis (that is bracket). In the given expression, we don’t have parenthesis. So, we step into the next thing that is, checking for exponents. The given expression also doesn’t have exponent terms.

Now we check for multiplication terms. In the second term of the given expression,

we have \[40\times 0\] which is equal to zero. So, the given expression changes to

\[\Rightarrow 40+0+1\]

Now, we have only additional operators in the expression. So, on simple addition of the terms present in the expression we get 41.

**Hence, 41 is the simplified value of the given expression \[40+40\cdot 0+1\].**

**Note:**One must clearly understand the PEMDAS rule before getting into the

question. A common error is assuming the answer to be 1, obtained from simple working from left to right hand side. That is, \[40+40\] gives 80 and on multiplying with 0 we get 0 itself. Hence, we are left with 1. While doing division, if we get a terminating decimal number then we have to round it.

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