Evaluate the expression (14⋅(5+3)(6−2))2. Show all your work.(4 points)
Math Short Answer Rubric (4 points)
Points Awarded Criteria
4
The answer is clear and correct.
The answer shows that the student used problem-solving skills and reasoning.
All work is shown or explained.
3
The answer is mostly correct. The student made small errors while solving.
The answer shows that the student used some problem-solving skills and reasoning.
Most work is shown or explained.
2
The answer is partially correct. The student made errors while solving.
The answer shows that the student used some problem-solving skills or reasoning.
Some work is shown or explained.
1
The answer is incorrect. The student made errors while solving.
The answer shows little problem-solving skills or reasoning.
Little or no work is shown.
0 The question is not answered.
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To evaluate the expression (14⋅(5+3)(6−2))2, we need to follow the order of operations (PEMDAS/BODMAS).
First, we'll simplify the expressions within the parentheses.
(5+3) = 8
(6−2) = 4
Now we have 14⋅8⋅4.
Next, we'll multiply 14 by 8 and then multiply the result by 4.
14⋅8 = 112
112⋅4 = 448.
Finally, we have 4482.
To evaluate this, we square the number 448.
4482 = 448 * 448 = 200704.
Therefore, the expression (14⋅(5+3)(6−2))2 evaluates to 200704.
To evaluate the expression (14⋅(5+3)(6−2))², let's follow the order of operations, also known as PEMDAS: parentheses, exponents, multiplication, division, addition, and subtraction.
Step 1: Simplify the expression inside the parentheses.
(5+3) = 8
(6-2) = 4
The expression now becomes:
(14⋅8⋅4)²
Step 2: Perform the multiplication.
14⋅8⋅4 = 448
The expression now becomes:
448²
Step 3: Evaluate the exponent.
448² = 200,704
Therefore, the value of the expression (14⋅(5+3)(6−2))² is 200,704.
To evaluate the expression (14⋅(5+3)(6−2))², we need to follow the order of operations (also known as PEMDAS or BIDMAS):
1. Start by evaluating the expressions inside the parentheses. Inside the first pair of parentheses, we have 5+3, which equals 8. Inside the second pair of parentheses, we have 6-2, which equals 4.
So now we have (14⋅8⋅4)².
2. Next, perform the multiplication operations from left to right. Multiply 14 by 8, and then multiply that result by 4:
14⋅8 = 112
112⋅4 = 448
Now we have (448)².
3. Finally, evaluate the exponent by multiplying 448 by itself:
448⋅448 = 200,704
Therefore, the expression (14⋅(5+3)(6−2))² equals 200,704.
To show all the work, we followed the order of operations step by step, evaluating parentheses first, then performing the multiplication, and finally evaluating the exponent. The final answer is 200,704.