How do you evaluate (7 x 4 + 5 to the second power) divided by (8 - 1 + 7 to the second power)?
(7 x 4 + 5 to the second power) divided by (8 - 1 + 7 to the second power)
= (7 x 4 + 5^2) divided by (8 - 1 + 7^2)
= (28 + 25)/(7 + 49)
= 53/56
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To evaluate the given expression: (7 x 4 + 5^2) ÷ (8 - 1 + 7^2), we follow the order of operations, which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).
Step 1: Evaluate any expressions inside parentheses or brackets.
There are no parentheses or brackets in the given expression, so we move on to the next step.
Step 2: Evaluate any exponents.
We have two exponents in the expression: 5^2 and 7^2.
5^2 means 5 raised to the power of 2, which is 25.
7^2 means 7 raised to the power of 2, which is 49.
After evaluating the exponents, our expression becomes: (7 x 4 + 25) ÷ (8 - 1 + 49).
Step 3: Perform any multiplications and divisions from left to right.
Now, we perform the multiplication: 7 x 4, which equals 28.
The expression becomes: (28 + 25) ÷ (8 - 1 + 49).
Step 4: Perform any additions and subtractions from left to right.
Next, we perform the addition and subtraction:
8 - 1 = 7
7 + 49 = 56
The expression becomes: (28 + 25) ÷ 56.
Step 5: Perform the final division operation.
Finally, we can perform the division: (28 + 25) ÷ 56.
28 + 25 = 53
Now, we divide 53 by 56: 53 ÷ 56 = 0.9464 (rounded to four decimal places).
Therefore, the value of the given expression is approximately 0.9464.