which of the following is an equivalent exspression to 1/2 (9-7^0) +(-29)^0?
1/2(-1)-1
1/2(2)+1
1/2(9-0)+0
1/2 (9-1)-1
The equivalent expression to 1/2 (9-7^0) +(-29)^0 is 1/2(9-0)+0.
7^0 = 1 not 0
To find an equivalent expression to 1/2(9-7^0) +(-29)^0, let's simplify each option one by one:
Option 1: 1/2(-1)-1
We can simplify this by multiplying and adding:
1/2(-1)-1 = -1/2 - 1 = -1/2 - 2/2 = -3/2
Option 2: 1/2(2)+1
Again, we can simplify by multiplying and adding:
1/2(2)+1 = 1+1 = 2
Option 3: 1/2(9-0)+0
Here, we can simplify by subtracting and multiplying:
1/2(9-0)+0 = 1/2(9)+0 = 9/2 + 0 = 9/2
Option 4: 1/2 (9-1)-1
Once again, we can simplify by subtracting and multiplying:
1/2 (9-1)-1 = 1/2(8) - 1 = 4 - 1 = 3
Comparing the simplified expressions to the original expression, we can see that the equivalent expression is represented by option 3: 1/2(9-0)+0, which simplifies to 9/2.
To find the equivalent expression, let's start by evaluating the individual parts of the expression step by step.
1. Simplify the exponent: 7^0 = 1. Any number raised to the power of zero equals 1.
Therefore, the expression becomes: 1/2 (9-1) + (-29)^0.
2. Evaluate (-29)^0: Any non-zero number raised to the power of zero equals 1.
Therefore, the expression becomes: 1/2 (9-1) + 1.
3. Simplify the subtraction inside the parentheses: 9-1 = 8.
The expression now becomes: 1/2 (8) + 1.
4. Multiply 1/2 by 8: 1/2 * 8 = 4.
The expression simplifies to: 4 + 1.
5. Add 4 and 1: 4 + 1 = 5.
So, the equivalent expression to 1/2 (9-7^0) + (-29)^0 is 5.