Use the order of operations to simplify each of the following :
a) 4*3^3- 54÷6+5^2
b)314-3 [2^5 -(9- 4 ) ^2 +3]^2
so, show us your work, and we'll check it.
A . 4 * 18 -54÷6+25
72-9 +26
72- 35
37
B.314-3[ 32-(9-16)+9
314-3[32 -9 -16+9
314 -96 -9-24
218+15 = 233
3^3 = 27, not 18
4 * 27 -54÷6+25
Just as multiplication/division are done left to right, so are addition and subtraction
108-9 +25
99+25
124
Besides the typo of 26, you did 72-(9+26), not 72-9+26
314-3 [2^5 -(9- 4 ) ^2 +3]^2
314-3 [2^5 - 5^2 +3]^2
314 - 3[32-25+3]^2
314 - 3[10]^2
314 - 3*100
314 - 300
14
I suggest you do some serious review of the order of valuation. Those parentheses are there for a reason!
To simplify the expressions using the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right), follow these steps:
a) Simplifying the expression: 4 * 3^3 - 54 ÷ 6 + 5^2
The first step is to evaluate the exponents:
3^3 = 3 * 3 * 3 = 27
5^2 = 5 * 5 = 25
Now let's substitute the values into the expression:
4 * 27 - 54 ÷ 6 + 25
The next step is to perform the multiplication and division from left to right:
4 * 27 = 108
54 ÷ 6 = 9
Substituting the values:
108 - 9 + 25
Finally, perform the addition and subtraction from left to right:
108 - 9 = 99
99 + 25 = 124
Therefore, the simplified expression is 124.
b) Simplifying the expression: 314 - 3 [2^5 - (9 - 4) ^2 + 3]^2
Start by simplifying inside the parentheses first:
9 - 4 = 5
Substituting the value into the expression:
314 - 3 [2^5 - 5^2 + 3]^2
Now evaluate the exponents:
2^5 = 2 * 2 * 2 * 2 * 2 = 32
5^2 = 5 * 5 = 25
Substituting the values:
314 - 3 [32 - 25 + 3]^2
Next, perform the addition and subtraction inside the brackets:
32 - 25 = 7
7 + 3 = 10
Substituting the value:
314 - 3 [10]^2
Now, evaluate the exponent inside the brackets:
10^2 = 10 * 10 = 100
Substituting the value:
314 - 3 * 100
To multiply, first multiply 3 by 100:
3 * 100 = 300
Substituting the value:
314 - 300
Finally, perform the subtraction:
314 - 300 = 14
Therefore, the simplified expression is 14.