Apply the Zero Power Rule to 9 x (-33)^0 + 3/2 (8 - 27^0)
In order to apply the Zero Power Rule, we need to simplify the exponent of zero. However, any number (except zero) raised to the power of zero equals 1. Therefore, we can simplify the expression as follows:
9 x (-33)^0 + 3/2 (8 - 27^0)
= 9 x 1 + 3/2 (8 - 1)
= 9 + 3/2 (7)
= 9 + 21/2
= 9 + 10.5
= 19.5
To apply the Zero Power Rule, we need to understand that any number raised to the power of 0 equals 1.
Let's break down the expression step-by-step:
1. Start with 9 x (-33)^0 + 3/2 (8 - 27^0)
2. According to the Zero Power Rule, (-33)^0 equals 1. So, the expression becomes:
9 x 1 + 3/2 (8 - 1)
3. Simplify further:
9 x 1 + 3/2 (7)
4. Multiply 9 by 1:
9 + 3/2 (7)
5. Multiply 3/2 by 7:
9 + 21/2
6. To add mixed numbers, we need to have the same denominator. To do so, multiply the whole number (9) by 2 to get 18/2:
18/2 + 21/2
7. Now, we can add the fractions:
(18 + 21)/2
8. Combine the numerators:
39/2
Therefore, the expression 9 x (-33)^0 + 3/2 (8 - 27^0) simplifies to 39/2.
To apply the Zero Power Rule, we need to understand what the rule is and how to use it. The Zero Power Rule states that any non-zero number raised to the power of zero is equal to 1. So, in any expression where a number is raised to the power of zero, the result is always 1.
Now, let's apply the Zero Power Rule to the given expression step by step:
1. Start by identifying the parts of the expression that involve a number raised to the power of zero.
In the expression 9 x (-33)^0 + 3/2 (8 - 27^0), we have two instances of a number raised to the power of zero. The first one is (-33)^0, and the second one is 27^0.
2. Apply the Zero Power Rule to generate simplified expressions.
The Zero Power Rule tells us that any number raised to the power of zero is equal to 1. So, we can replace (-33)^0 with 1, and 27^0 with 1.
Now the expression becomes 9 x 1 + 3/2 (8 - 1).
3. Simplify the remaining expression.
The next step is to simplify the expression further. In the expression 9 x 1 + 3/2 (8 - 1), we can begin by solving any operations inside parentheses.
The expression in the parentheses is 8 - 1, which gives us 7.
So the expression becomes 9 x 1 + 3/2 (7).
Next, evaluate the multiplication and division from left to right.
9 x 1 is simply 9, and then we have 3/2 x 7.
To multiply 3/2 by 7, we multiply the numerators (3 x 7) and the denominators (2), giving us 21/2.
So, the final simplified expression is 9 + 21/2.
To add 9 and 21/2, we need to find a common denominator, which is 2. Adjusting 9 to have a denominator of 2, we get 18/2.
Now, we can add: 18/2 + 21/2 = (18 + 21)/2 = 39/2.
Therefore, the simplified expression using the Zero Power Rule is 39/2.