Evaluate the expression (1^4⋅(5+3)(6−2))2 . Show all your work.(4 points)
First, we simplify the expression inside the parentheses:
(5+3) = 8
(6-2) = 4
So now we have:
(1^4⋅8⋅4)2
Next, we simplify the expression inside the first set of parentheses:
Since 1 raised to any power is still 1, the expression becomes:
(1⋅8⋅4)2
Now we simplify the expression inside the second set of parentheses:
8⋅4 = 32
So now we have:
(32)2
Finally, we evaluate the exponent:
32^2 = 32 * 32 = 1024
Therefore, the evaluated expression is 1024.
To evaluate the expression (1^4⋅(5+3)(6−2))2, follow the order of operations: parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).
First, simplify the expression within the parentheses:
(5 + 3) = 8
(6 - 2) = 4
Next, substitute the simplifications back into the original expression:
(1^4 * 8 * 4)^2
Simplify the exponent:
1^4 = 1
Apply multiplication:
1 * 8 * 4 = 32
Substitute the multiplication result back into the original expression:
(32)^2
Square the value:
32^2 = 1024
Therefore, (1^4⋅(5+3)(6−2))2 = 1024.
To evaluate the expression (1^4⋅(5+3)(6−2))2, we need to follow the order of operations, which is often remembered by the acronym PEMDAS.
1. Start by simplifying any operations within parentheses: (5+3) = 8 and (6−2) = 4.
2. Replace the expressions within the parentheses with their simplified values: (1^4⋅8⋅4)2.
3. Next, solve any exponents: 1^4 = 1, so the expression becomes (1⋅8⋅4)2.
4. Now, perform the multiplication: 1⋅8⋅4 = 32, so the expression becomes (32)2.
5. Finally, evaluate the expression within parentheses: (32)2 = 32^2 = 1024.
Therefore, the value of the expression (1^4⋅(5+3)(6−2))2 is 1024.