Question

Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)^0+3/2(8−27^0).

Answer 1

[AI-generated answer — Bot GPT 3.5]

By applying the Zero Power Rule, any non-zero number raised to the power of 0 equals 1. Therefore, we have:

9⋅(−33)^0 + 3/2(8−27^0)

Since any number raised to the power of 0 equals 1, (-33)^0 equals 1. Substituting this value, we get:

9⋅1 + 3/2(8−1)

Simplifying further:

9 + 3/2(7)

Now, let's calculate the expression in the parentheses:

9 + 3/2 * 7

Multiplying 3/2 by 7:

9 + 21/2

In order to add the fractions, we need a common denominator:

9 + 21/2 = 18/2 + 21/2 = 39/2

Therefore, the equivalent expression is 39/2.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To apply the Zero Power Rule, we need to know that any non-zero number raised to the power of zero is equal to 1. Additionally, any zero raised to the power of zero is considered undefined.

Let's break down the given expression and apply the rule step-by-step:

1. Start with the expression: 9⋅(−33)^0 + 3/2(8−27^0).
2. According to the Zero Power Rule, any number raised to the power of zero is equal to 1. Therefore, we can simplify (−33)^0 to 1: 9⋅1 + 3/2(8−27^0).
3. Multiply 9 by 1: 9 + 3/2(8−27^0).
4. Simplify 27^0 to 1: 9 + 3/2(8−1).
5. Subtract inside the parentheses: 9 + 3/2(7).
6. Multiply 3/2 by 7: 9 + (3/2)⋅ 7.
7. Multiply 3/2 by 7: 9 + (21/2).
8. Find a common denominator: 9 + 21/2 = 9 + 10.5 = 19.5.

Therefore, the equivalent expression is 19.5.