Asked by yayy

Which of the following is developed to result in the answer of 1?
5^0+9^0
3 (8^0)
13-(7.42)^0
(-2.97)^0
Answered by yayy
Which of the following shows the correct process of solving -3^0+4.5?
-3^0+4.5=(-3)^0+4.5=1+4.5=5.5

-3^0+4.5=-3+4.5=1.5

-3^0+4.5=-3.0+4.5=0+4.5=4.5

-3^0+4.5=-1 times 3^0+4.5=-1 times 1 +4.5=-1+4.5=3.5
Answered by yayy
Which of the following is an equivalent expression to 7 over (-5.3)^0 +4 times 9 when applying the Zero Power Rule?
7/1 + 4 times 9
7/5.3^0 + 36
7/5.3 + 4 times 9
7/0 + 4 times 9
Answered by yayy
there is only one answer
Answered by yayy
Which of the following is an equivalent expression to 1/2 (9-7^0)+(-29)^0
1/2(9-1)-1
1/2(9-1)+1
1/2(2)+1
1/2(9-0)+0
Answered by yayy
Show the correct process of solving -4(3+12^0)+15^0 by generating an equivalent expression using the Zero Power Rule.
Answered by GPT-4o mini
To determine which of the expressions results in an answer of 1, we evaluate each one.

1. **\(5^0 + 9^0\)**:
- Any non-zero number raised to the power of 0 is equal to 1.
- Therefore, \(5^0 = 1\) and \(9^0 = 1\).
- Thus, \(5^0 + 9^0 = 1 + 1 = 2\).

2. **\(3 (8^0)\)**:
- Again, any non-zero number raised to the power of 0 is 1.
- Thus, \(8^0 = 1\).
- Therefore, \(3 (8^0) = 3 \times 1 = 3\).

3. **\(13 - (7.42)^0\)**:
- Here, \((7.42)^0 = 1\).
- So, \(13 - (7.42)^0 = 13 - 1 = 12\).

4. **\((-2.97)^0\)**:
- Regardless of the base (as long as it's not 0), any non-zero number raised to the power of 0 is equal to 1.
- Therefore, \((-2.97)^0 = 1\).

After evaluating all expressions:

- \(5^0 + 9^0 = 2\)
- \(3 (8^0) = 3\)
- \(13 - (7.42)^0 = 12\)
- \((-2.97)^0 = 1\)

The only expression that results in an answer of 1 is:

\[
\boxed{(-2.97)^0}
\]
Answered by GPT-4o mini
To solve the expression \(-3^0 + 4.5\), we need to evaluate each part carefully.

1. The part \(-3^0\):
- The exponentiation here means \(3^0\), and since \(3\) is a positive number, \(3^0 = 1\).
- Thus, \(-3^0 = -1\).

2. Putting it all together:
- We have \(-1 + 4.5\).

Now, let's evaluate \( -1 + 4.5\):
\[
-1 + 4.5 = 3.5
\]

Now let's examine the proposed solutions:

1. **First option:**
\(-3^0 + 4.5 = (-3)^0 + 4.5 = 1 + 4.5 = 5.5\)
This is incorrect because \(-3^0\) evaluates to \(-1\), not \((-3)^0\).

2. **Second option:**
\(-3^0 + 4.5 = -3 + 4.5 = 1.5\)
This is incorrect because it incorrectly evaluates \(-3^0\).

3. **Third option:**
\(-3^0+4.5 = -3.0 + 4.5 = 0 + 4.5 = 4.5\)
This is also incorrect for the same reason.

4. **Fourth option:**
\(-3^0 + 4.5 = -1 \cdot 3^0 + 4.5 = -1 \cdot 1 + 4.5 = -1 + 4.5 = 3.5\)
This is correct because it properly evaluates \(-3^0\) as \(-1\).

Based on this evaluation, the correct process of solving \(-3^0 + 4.5\) is shown in the **fourth option**:

\[
\boxed{-3^0 + 4.5 = -1 \cdot 3^0 + 4.5 = -1 + 4.5 = 3.5}
\]
Answered by GPT-4o mini
To solve the expression \( \frac{7}{(-5.3)^0} + 4 \times 9 \) by applying the Zero Power Rule, we first need to evaluate \((-5.3)^0\).

According to the Zero Power Rule, any non-zero number raised to the power of 0 equals 1. Therefore, since \(-5.3\) is not zero:

\[
(-5.3)^0 = 1
\]

Substituting this back into our expression, we get:

\[
\frac{7}{(-5.3)^0} + 4 \times 9 = \frac{7}{1} + 4 \times 9
\]

Now, simplifying the expression:

\[
\frac{7}{1} = 7
\]
And \(4 \times 9 = 36\), so:

\[
7 + 36
\]

This confirms that:

\[
\frac{7}{(-5.3)^0} + 4 \times 9 = 7 + 36
\]

Now, let's evaluate the given options to find an equivalent expression:

1. **Option 1:** \( \frac{7}{1} + 4 \times 9 \)
This is equivalent to \(7 + 36\), so it is correct.

2. **Option 2:** \( \frac{7}{5.3^0} + 36 \)
Here \( 5.3^0 \) is also 1, so this equals \(7 + 36\) as well, thus it is correct.

3. **Option 3:** \( \frac{7}{5.3} + 4 \times 9 \)
This is not correct; it does not account for the Zero Power Rule correctly.

4. **Option 4:** \( \frac{7}{0} + 4 \times 9 \)
This is incorrect because \((-5.3)^0\) is not 0; it is 1.

Based on the evaluation, the correct equivalent expressions are:

- **Option 1:** \( \frac{7}{1} + 4 \times 9 \)
- **Option 2:** \( \frac{7}{(-5.3)^0} + 36 \)

Thus, the correct expressions that show equivalence when applying the Zero Power Rule are:
\[
\boxed{\frac{7}{1} + 4 \times 9} \quad \text{and} \quad \boxed{\frac{7}{5.3^0} + 36}
\]
Answered by GPT-4o mini
Thank you for your patience, and I understand now that you are looking for a single answer that best reflects the original expression \( \frac{7}{(-5.3)^0} + 4 \times 9 \) when applying the Zero Power Rule.

As we established:
- \((-5.3)^0 = 1\), so \( \frac{7}{(-5.3)^0} = \frac{7}{1} = 7\).
- Then \(4 \times 9 = 36\), therefore the expression becomes \(7 + 36\).

We will again evaluate the options you provided:

1. **Option 1:** \( \frac{7}{1} + 4 \times 9 \)
This is indeed \(7 + 36\) since \(\frac{7}{1} = 7\).

2. **Option 2:** \( \frac{7}{5.3^0} + 36 \)
This is also equivalent to \(7 + 36\) since \(5.3^0 = 1\).

3. **Option 3:** \( \frac{7}{5.3} + 4 \times 9 \)
This is not equivalent to the original since it does not apply the Zero Power Rule correctly.

4. **Option 4:** \( \frac{7}{0} + 4 \times 9 \)
This is incorrect as the denominator cannot be zero.

Given that both Option 1 and Option 2 could be considered equivalent to the application of the Zero Power Rule, however, if only one option must be selected:

The clearest representation of the expression in relation to the original problem is **Option 1**:

\[
\boxed{\frac{7}{1} + 4 \times 9}
\]

This option directly indicates applying the Zero Power Rule and simplifies the original expression most clearly.
Answered by GPT-4o mini
To find an equivalent expression for \( \frac{1}{2} (9 - 7^0) + (-29)^0 \), we should evaluate each part of the expression.

1. **Calculate \(7^0\)**:
- According to the Zero Power Rule, \(7^0 = 1\).

2. **Calculate \((-29)^0\)**:
- Similarly, \((-29)^0 = 1\) because any non-zero number raised to the power of 0 is equal to 1.

Now we can substitute these values back into the expression:

\[
\frac{1}{2} (9 - 7^0) + (-29)^0 = \frac{1}{2} (9 - 1) + 1
\]

Now simplify it:

\[
= \frac{1}{2} (8) + 1
\]
\[
= 4 + 1 = 5
\]

Now we need to check each of the provided options to determine which one simplifies to \(5\):

1. **Option 1:** \(\frac{1}{2} (9 - 1) - 1\)
\[
= \frac{1}{2} (8) - 1 = 4 - 1 = 3 \quad \text{(not equivalent)}
\]

2. **Option 2:** \(\frac{1}{2} (9 - 1) + 1\)
\[
= \frac{1}{2} (8) + 1 = 4 + 1 = 5 \quad \text{(equivalent)}
\]

3. **Option 3:** \(\frac{1}{2} (2) + 1\)
\[
= 1 + 1 = 2 \quad \text{(not equivalent)}
\]

4. **Option 4:** \(\frac{1}{2} (9 - 0) + 0\)
\[
= \frac{1}{2} (9) + 0 = 4.5 \quad \text{(not equivalent)}
\]

Thus, the only equivalent expression to \( \frac{1}{2} (9 - 7^0) + (-29)^0 \) is:

\[
\boxed{\frac{1}{2} (9 - 1) + 1}
\]
Answered by GPT-4o mini
To solve the expression \(-4(3 + 12^0) + 15^0\) using the Zero Power Rule, we start by evaluating the terms \(12^0\) and \(15^0\).

1. **Applying the Zero Power Rule**:
- According to the Zero Power Rule, any non-zero number raised to the power of 0 equals 1.
- Thus, \(12^0 = 1\) and \(15^0 = 1\).

Now substitute these values back into the original expression:

\[
-4(3 + 12^0) + 15^0 = -4(3 + 1) + 1
\]

2. **Simplifying the expression**:
- First, compute inside the parentheses: \(3 + 1 = 4\).
- Now substitute this back into the expression:

\[
-4(4) + 1
\]

3. **Continuing with the calculations**:
- Now calculate \(-4(4)\):
\[
-4 \cdot 4 = -16
\]

- Finally, add 1:
\[
-16 + 1 = -15
\]

### Summary of the equivalent expression:

The equivalent expression can be shown as:

\[
-4(3 + 12^0) + 15^0 = -4(3 + 1) + 1 = -4(4) + 1 = -16 + 1 = -15
\]

So, the final answer after applying the Zero Power Rule and simplifying is:

\[
\boxed{-15}
\]

This is the correct process to solve the expression \(-4(3 + 12^0) + 15^0\) using the Zero Power Rule.