Evaluate the expression (1^4⋅(5+3)/(6−2))^2. Show all your work.
The expression is (1^4*(5+3)/(6-2))^2.
First, compute the operations inside the parentheses.
1^4 = 1.
5 + 3 = 8.
6 - 2 = 4.
This simplifies the expression to (1*8/4)^2.
Next, perform the multiplication and division from left to right.
1*8 = 8.
8/4 = 2.
This simplifies the expression to 2^2.
Finally, calculate the exponent.
2^2 = 4.
The expression (1^4*(5+3)/(6-2))^2 evaluates to 4.
To evaluate the expression (1^4⋅(5+3)/(6−2))^2, we need to follow the order of operations, which is often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division - from left to right, Addition and Subtraction - from left to right).
Let's break it down step-by-step.
Step 1: Inside the parentheses, perform the addition:
5 + 3 = 8.
So, the expression becomes:
(1^4⋅8/(6−2))^2.
Step 2: Inside the parentheses, perform the subtraction:
6 - 2 = 4.
So, the expression becomes:
(1^4⋅8/4)^2.
Step 3: Inside the exponents, simplify:
1^4 = 1.
So, the expression becomes:
(1⋅8/4)^2.
Step 4: Inside the multiplication, perform the calculation:
1⋅8 = 8.
So, the expression becomes:
(8/4)^2.
Step 5: Inside the division, perform the calculation:
8/4 = 2.
So, the expression becomes:
2^2.
Step 6: Inside the exponents, calculate:
2^2 = 4.
Therefore, the value of the expression (1^4⋅(5+3)/(6−2))^2 is 4.
To evaluate the given expression, we need to follow the order of operations which is often represented by the acronym PEMDAS (Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction). Let's break down the expression step by step:
Step 1: Calculate the values within parentheses.
- The expression inside the parentheses is (5+3)/(6-2).
- Within the parentheses, we can first perform the addition and subtraction: 5+3 = 8, and 6-2 = 4.
- So the expression becomes 8/4.
Step 2: Simplify the division.
- 8 divided by 4 equals 2.
- So the expression now becomes 2^2.
Step 3: Evaluate the exponent.
- 2 raised to the power of 2 means multiplying 2 by itself: 2^2 = 2 * 2 = 4.
Therefore, the value of the given expression is 4.
In summary:
(1^4⋅(5+3)/(6−2))^2
= (1^4⋅8/4)^2
= (1⋅8/4)^2
= 2^2
= 4