Question

rodrigo tried to evaluate an expression. here is his work:
$26 - (2^4 - 10 \div 2)$
$= 26 - (16 - 10 \div 2)$ step 1
$= 26 - (16 - 5)$ step 2
$= 26 - 11$ step 3
$= 15$ step 4
is rodrigos work correct?
no, rodrigo made a mistake going from step 1 to step 2. rodrigo should have subtracted 10 from 16 before dividing. the order of operations says to divide and subtract from left to right.
no, rodrigo made a mistake going from step 2 to step 3. rodrigo should have subtracted 16 from 26 instead of subtracting 5 from 16. the order of operations says to subtract from left to right.
yes, rodrigos work is correct.

Explanation:

Step1: Calculate the exponent and division inside the parentheses

According to the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left - to - right), Addition and Subtraction (from left - to - right)), for the expression \(26-(2^{4}-10\div2)\), first calculate \(2^{4}=16\) and \(10\div2 = 5\). So the expression becomes \(26-(16 - 5)\) (Rodrigo's Step 2 is correct as he did the division \(10\div2\) before subtraction inside the parentheses).

Step2: Calculate the subtraction inside the parentheses

Now, calculate \(16-5=11\), and the expression is \(26 - 11\) (Rodrigo's Step 3 is correct).

Step3: Calculate the final subtraction

Finally, \(26-11 = 15\) (Rodrigo's Step 4 is correct).

Answer:

Yes, Rodrigo's work is correct.