9.(-33)0+3/2(8-27^0).
To solve this expression, we will follow the order of operations (PEMDAS/BODMAS):
1. Start with the operations inside the parentheses: (-27^0)
- Anything raised to the power of 0 is always 1.
- So, (-27^0) becomes (-27^1) which is equal to -27.
The expression becomes: (-33)0 + 3/2(8 - (-27))
2. Next, perform the subtraction inside the parentheses: (8 - (-27))
- Subtracting a negative number is the same as adding the positive number.
- So, (8 - (-27)) becomes (8 + 27) which is equal to 35.
The expression becomes: (-33)0 + 3/2(35)
3. Now, multiply 3/2 by 35:
- Multiply the numerator and denominator separately: 3 x 35 = 105 and 2 x 1 = 2.
- So, 3/2(35) becomes 105/2 or 52.5.
The expression becomes: (-33)0 + 52.5
4. Next, perform the multiplication: (-33)0
- Anything raised to the power of 0 is always 1.
- So, (-33)0 becomes 1.
The expression becomes: 1 + 52.5
5. Finally, perform the addition: 1 + 52.5
- 1 + 52.5 equals 53.5.
The final answer is 53.5.
To solve this expression step-by-step, let's break it down:
Step 1: Simplify the exponent
27^0 = 1 since any number raised to the power of 0 is equal to 1.
Step 2: Calculate the multiplication and division from left to right
3/2 * (8 - 1) = 3/2 * 7 = 21/2 or 10.5
Step 3: Multiply the remaining terms
(-33) * 0 + 10.5 = 0 + 10.5 = 10.5
Therefore, the value of the given expression is 10.5.
To solve this expression, we need to follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division - from left to right, and Addition and Subtraction - from left to right). Let's break down the expression step by step:
Step 1: Parentheses
We have (-33)0, which means we need to perform any operations inside the parentheses first. Anything raised to the power of 0 is equal to 1, so (-33)0 = 1.
Step 2: Exponents
There are no other exponents in the expression, so we move to the next step.
Step 3: Multiplication and Division
We have 3/2, so we need to divide 3 by 2. The result is 1.5 (or 3/2 = 1.5).
Step 4: Multiplication and Division (continued)
Now we have 1.5 multiplied by (8 - 27^0). Since the exponent 0 was already evaluated as 1 earlier, the expression becomes 1.5 multiplied by (8 - 1).
Step 5: Multiplication and Division (continued)
We need to evaluate (8 - 1) inside the parentheses, which gives us 7. So now the expression becomes 1.5 multiplied by 7.
Step 6: Multiplication and Division (continued)
Multiplying 1.5 by 7 gives us the final result: 1.5 * 7 = 10.5.
Therefore, the answer to the given expression is 10.5.