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Original Question
Which of the following is developed to result in the answer of 1? 5^0+9^0 (-2.97)^0 3(8^0) 13-(7.42)^0Question
which of the following is developed to result in the answer of 1?
a. 5^0 + 9^0
b. (-2.97)^0
c. 3(8^0)
d. 13 - (7.42)^0
a. 5^0 + 9^0
b. (-2.97)^0
c. 3(8^0)
d. 13 - (7.42)^0
Answers
Answer
Which of the following shows the correct process of solving.
-3^0 + 4.5?
a. -3^0 + 4.5 = -3 x 0 + 4.5 = 0 + 4.5 = 4.5
b. -3^0 + 4.5 = (-3)^0 + 4.5 = 1 + 4.5 = 5.5
c. -3^0 + 4.5 = -3 + 4.5 = 1.5
d. -3^0 + 4.5 = -1 x 3^0 + 4.5 = -1 x 1 + 4.5 = -1 + 4.5 = 3.5
-3^0 + 4.5?
a. -3^0 + 4.5 = -3 x 0 + 4.5 = 0 + 4.5 = 4.5
b. -3^0 + 4.5 = (-3)^0 + 4.5 = 1 + 4.5 = 5.5
c. -3^0 + 4.5 = -3 + 4.5 = 1.5
d. -3^0 + 4.5 = -1 x 3^0 + 4.5 = -1 x 1 + 4.5 = -1 + 4.5 = 3.5
Answer
Which of the following is an equivalent expression to equivalent expression to 7/(-5.3)^0 + 4 x 9 when applying the Zero Power Rule?
a. 7/1 + 4 x 9
b. 7/0 + 4 x 9
c. 7/5.3^0 + 36
d. 7/5.3 + 4 x 9
a. 7/1 + 4 x 9
b. 7/0 + 4 x 9
c. 7/5.3^0 + 36
d. 7/5.3 + 4 x 9
Answer
Which of the following is an equivalent expression to 1/2 (9 - 7^0) + (-29)^0?
a. 1/2 (9 - 0) + 0
b. 1/2 (2) + 1
c. 1/2 (9 - 1) + 1
d. 1/2 (9 - 1) -1
a. 1/2 (9 - 0) + 0
b. 1/2 (2) + 1
c. 1/2 (9 - 1) + 1
d. 1/2 (9 - 1) -1
Answer
Which of the following shows the correct process of solving -4 ( 3 + 12^0) + 15^0 by generating an equivalent expression using the zero power rule?
a. -4 (3 + 12^0) + 15 = -4 (3 + 1) + 1 = -4 x 4 + 1 = -4 x 5 = -20
b. -4 (3 + 12^0) + 15^0 = -4 (15) + 1 = -60 + 1 = -59
c. -4 (3 + 12^0) + 15^0 = -4 (15) + 15 = -60 + 15 = -45
d. -4 (3 + 12^0) + 15^0 = -4 (3 + 1)
a. -4 (3 + 12^0) + 15 = -4 (3 + 1) + 1 = -4 x 4 + 1 = -4 x 5 = -20
b. -4 (3 + 12^0) + 15^0 = -4 (15) + 1 = -60 + 1 = -59
c. -4 (3 + 12^0) + 15^0 = -4 (15) + 15 = -60 + 15 = -45
d. -4 (3 + 12^0) + 15^0 = -4 (3 + 1)
Answered by
GPT-4o mini
To determine which of the given options results in the answer of 1, let's evaluate each expression:
a. \(5^0 + 9^0\)
Using the property that any non-zero number raised to the power of 0 is 1:
\[
5^0 = 1 \quad \text{and} \quad 9^0 = 1
\]
So,
\[
5^0 + 9^0 = 1 + 1 = 2
\]
b. \((-2.97)^0\)
Using the same property:
\[
(-2.97)^0 = 1
\]
c. \(3(8^0)\)
Again, using the property:
\[
8^0 = 1
\]
So,
\[
3(8^0) = 3(1) = 3
\]
d. \(13 - (7.42)^0\)
Using the property:
\[
(7.42)^0 = 1
\]
So,
\[
13 - (7.42)^0 = 13 - 1 = 12
\]
Now, summarizing the results:
- a: 2
- b: 1
- c: 3
- d: 12
The correct answer is **b. \((-2.97)^0\)**.
a. \(5^0 + 9^0\)
Using the property that any non-zero number raised to the power of 0 is 1:
\[
5^0 = 1 \quad \text{and} \quad 9^0 = 1
\]
So,
\[
5^0 + 9^0 = 1 + 1 = 2
\]
b. \((-2.97)^0\)
Using the same property:
\[
(-2.97)^0 = 1
\]
c. \(3(8^0)\)
Again, using the property:
\[
8^0 = 1
\]
So,
\[
3(8^0) = 3(1) = 3
\]
d. \(13 - (7.42)^0\)
Using the property:
\[
(7.42)^0 = 1
\]
So,
\[
13 - (7.42)^0 = 13 - 1 = 12
\]
Now, summarizing the results:
- a: 2
- b: 1
- c: 3
- d: 12
The correct answer is **b. \((-2.97)^0\)**.
Answered by
GPT-4o mini
To correctly evaluate the expression \(-3^0 + 4.5\), we first need to understand the exponentiation rules.
The expression \(-3^0\) does not mean \((-3)^0\). According to the order of operations, \( -3^0 \) is interpreted as \(-(3^0)\). Notably, the exponent applies only to the number immediately to its left, which is 3, not the negative sign:
1. Calculate \(3^0\):
\[
3^0 = 1
\]
2. Apply the negative:
\[
-3^0 = -1
\]
3. Now, we can add 4.5:
\[
-1 + 4.5 = 3.5
\]
Now let’s analyze the options provided:
a. \(-3^0 + 4.5 = -3 \times 0 + 4.5 = 0 + 4.5 = 4.5\)
(This is incorrect since it incorrectly treats \(-3^0\) as \(-3 \times 0\).)
b. \(-3^0 + 4.5 = (-3)^0 + 4.5 = 1 + 4.5 = 5.5\)
(This is incorrect as it treats the exponent incorrectly as applying to the negative.)
c. \(-3^0 + 4.5 = -3 + 4.5 = 1.5\)
(This is incorrect since it does not apply the exponent correctly.)
d. \(-3^0 + 4.5 = -1 \times 3^0 + 4.5 = -1 \times 1 + 4.5 = -1 + 4.5 = 3.5\)
(This correctly calculates \(-3^0\) as \(-1\) and then adds \(4.5\), leading to \(3.5\).)
Thus, the correct answer is **d. \(-3^0 + 4.5 = -1 \times 3^0 + 4.5 = -1 \times 1 + 4.5 = -1 + 4.5 = 3.5\)**.
The expression \(-3^0\) does not mean \((-3)^0\). According to the order of operations, \( -3^0 \) is interpreted as \(-(3^0)\). Notably, the exponent applies only to the number immediately to its left, which is 3, not the negative sign:
1. Calculate \(3^0\):
\[
3^0 = 1
\]
2. Apply the negative:
\[
-3^0 = -1
\]
3. Now, we can add 4.5:
\[
-1 + 4.5 = 3.5
\]
Now let’s analyze the options provided:
a. \(-3^0 + 4.5 = -3 \times 0 + 4.5 = 0 + 4.5 = 4.5\)
(This is incorrect since it incorrectly treats \(-3^0\) as \(-3 \times 0\).)
b. \(-3^0 + 4.5 = (-3)^0 + 4.5 = 1 + 4.5 = 5.5\)
(This is incorrect as it treats the exponent incorrectly as applying to the negative.)
c. \(-3^0 + 4.5 = -3 + 4.5 = 1.5\)
(This is incorrect since it does not apply the exponent correctly.)
d. \(-3^0 + 4.5 = -1 \times 3^0 + 4.5 = -1 \times 1 + 4.5 = -1 + 4.5 = 3.5\)
(This correctly calculates \(-3^0\) as \(-1\) and then adds \(4.5\), leading to \(3.5\).)
Thus, the correct answer is **d. \(-3^0 + 4.5 = -1 \times 3^0 + 4.5 = -1 \times 1 + 4.5 = -1 + 4.5 = 3.5\)**.
Answered by
GPT-4o mini
To solve the expression \( \frac{7}{(-5.3)^0} + 4 \times 9 \) using the Zero Power Rule, we first need to apply the Zero Power Rule correctly. The rule states that any non-zero number raised to the power of 0 is equal to 1.
Thus, we can simplify \( (-5.3)^0 \):
\[
(-5.3)^0 = 1
\]
Now, substituting this back into the expression, we have:
\[
\frac{7}{(-5.3)^0} + 4 \times 9 = \frac{7}{1} + 4 \times 9
\]
Now we can calculate \( 4 \times 9 \):
\[
4 \times 9 = 36
\]
Therefore, the expression simplifies to:
\[
\frac{7}{1} + 36 = 7 + 36 = 43
\]
Now, let's look at the options provided:
a. \( \frac{7}{1} + 4 \times 9 \)
b. \( \frac{7}{0} + 4 \times 9 \)
c. \( \frac{7}{5.3^0} + 36 \)
d. \( \frac{7}{5.3} + 4 \times 9 \)
Now, let's analyze these options:
- **Option a:** \( \frac{7}{1} + 4 \times 9 \) correctly simplifies to \( 7 + 36 \).
- **Option b:** \( \frac{7}{0} + 4 \times 9 \) is undefined because division by zero is not allowed.
- **Option c:** \( \frac{7}{5.3^0} + 36 \) is equivalent to \( \frac{7}{1} + 36 \), which also simplifies to \( 7 + 36 \).
- **Option d:** \( \frac{7}{5.3} + 4 \times 9 \) does not simplify to the same expression and is not equivalent.
Thus, the equivalent expressions based on applying the Zero Power Rule are:
- **a. \( \frac{7}{1} + 4 \times 9 \)**
- **c. \( \frac{7}{5.3^0} + 36 \)**
Both options **a** and **c** are equivalent expressions.
Thus, we can simplify \( (-5.3)^0 \):
\[
(-5.3)^0 = 1
\]
Now, substituting this back into the expression, we have:
\[
\frac{7}{(-5.3)^0} + 4 \times 9 = \frac{7}{1} + 4 \times 9
\]
Now we can calculate \( 4 \times 9 \):
\[
4 \times 9 = 36
\]
Therefore, the expression simplifies to:
\[
\frac{7}{1} + 36 = 7 + 36 = 43
\]
Now, let's look at the options provided:
a. \( \frac{7}{1} + 4 \times 9 \)
b. \( \frac{7}{0} + 4 \times 9 \)
c. \( \frac{7}{5.3^0} + 36 \)
d. \( \frac{7}{5.3} + 4 \times 9 \)
Now, let's analyze these options:
- **Option a:** \( \frac{7}{1} + 4 \times 9 \) correctly simplifies to \( 7 + 36 \).
- **Option b:** \( \frac{7}{0} + 4 \times 9 \) is undefined because division by zero is not allowed.
- **Option c:** \( \frac{7}{5.3^0} + 36 \) is equivalent to \( \frac{7}{1} + 36 \), which also simplifies to \( 7 + 36 \).
- **Option d:** \( \frac{7}{5.3} + 4 \times 9 \) does not simplify to the same expression and is not equivalent.
Thus, the equivalent expressions based on applying the Zero Power Rule are:
- **a. \( \frac{7}{1} + 4 \times 9 \)**
- **c. \( \frac{7}{5.3^0} + 36 \)**
Both options **a** and **c** are equivalent expressions.
Answered by
GPT-4o mini
To simplify the expression \( \frac{1}{2} (9 - 7^0) + (-29)^0 \), we first evaluate the components using the properties of exponents.
1. **Evaluate \( 7^0 \)**:
\[
7^0 = 1
\]
2. **Evaluate \( (-29)^0 \)**:
\[
(-29)^0 = 1
\]
Now we can substitute these values into the expression:
\[
\frac{1}{2} (9 - 1) + 1
\]
Next, simplify \( 9 - 1 \):
\[
9 - 1 = 8
\]
Now substitute back into the expression:
\[
\frac{1}{2} (8) + 1
\]
\[
= 4 + 1 = 5
\]
Now, let's evaluate each of the given options:
a. \( \frac{1}{2} (9 - 0) + 0 \)
- This simplifies to \( \frac{1}{2} (9) + 0 = 4.5 + 0 = 4.5 \)
b. \( \frac{1}{2} (2) + 1 \)
- This simplifies to \( 1 + 1 = 2 \)
c. \( \frac{1}{2} (9 - 1) + 1 \)
- This simplifies to \( \frac{1}{2} (8) + 1 = 4 + 1 = 5 \)
d. \( \frac{1}{2} (9 - 1) - 1 \)
- This simplifies to \( \frac{1}{2} (8) - 1 = 4 - 1 = 3 \)
Now, comparing the results:
- a: 4.5
- b: 2
- c: 5
- d: 3
The equivalent expression to \( \frac{1}{2} (9 - 7^0) + (-29)^0 \) simplifies to **5**, which corresponds to option **c: \( \frac{1}{2} (9 - 1) + 1 \)**.
1. **Evaluate \( 7^0 \)**:
\[
7^0 = 1
\]
2. **Evaluate \( (-29)^0 \)**:
\[
(-29)^0 = 1
\]
Now we can substitute these values into the expression:
\[
\frac{1}{2} (9 - 1) + 1
\]
Next, simplify \( 9 - 1 \):
\[
9 - 1 = 8
\]
Now substitute back into the expression:
\[
\frac{1}{2} (8) + 1
\]
\[
= 4 + 1 = 5
\]
Now, let's evaluate each of the given options:
a. \( \frac{1}{2} (9 - 0) + 0 \)
- This simplifies to \( \frac{1}{2} (9) + 0 = 4.5 + 0 = 4.5 \)
b. \( \frac{1}{2} (2) + 1 \)
- This simplifies to \( 1 + 1 = 2 \)
c. \( \frac{1}{2} (9 - 1) + 1 \)
- This simplifies to \( \frac{1}{2} (8) + 1 = 4 + 1 = 5 \)
d. \( \frac{1}{2} (9 - 1) - 1 \)
- This simplifies to \( \frac{1}{2} (8) - 1 = 4 - 1 = 3 \)
Now, comparing the results:
- a: 4.5
- b: 2
- c: 5
- d: 3
The equivalent expression to \( \frac{1}{2} (9 - 7^0) + (-29)^0 \) simplifies to **5**, which corresponds to option **c: \( \frac{1}{2} (9 - 1) + 1 \)**.
Answered by
GPT-4o mini
To simplify the expression \(-4 (3 + 12^0) + 15^0\) using the zero power rule, we will apply the rule correctly.
1. **Evaluate \(12^0\)**:
\[
12^0 = 1
\]
2. **Evaluate \(15^0\)**:
\[
15^0 = 1
\]
Now we can substitute these values back into the original expression:
\[
-4 (3 + 12^0) + 15^0 = -4 (3 + 1) + 1
\]
Next, simplify \(3 + 1\):
\[
= -4 (4) + 1
\]
Now, calculate \(-4 \times 4\):
\[
= -16 + 1
\]
Finally, simplify:
\[
-16 + 1 = -15
\]
Now, let's analyze each option given to see which one corresponds to this correct process.
**a.** \(-4 (3 + 12^0) + 15 = -4 (3 + 1) + 1 = -4 \times 4 + 1 = -4 \times 5 = -20\)
(This is incorrect. It states \(-4 \times 5\) instead of \(-4 \times 4\).)
**b.** \(-4 (3 + 12^0) + 15^0 = -4 (15) + 1 = -60 + 1 = -59\)
(This is incorrect. It does not evaluate \(3 + 1\) correctly.)
**c.** \(-4 (3 + 12^0) + 15^0 = -4 (15) + 15 = -60 + 15 = -45\)
(This is incorrect as it also does not evaluate \(3 + 1\) correctly.)
**d.** \(-4 (3 + 12^0) + 15^0 = -4 (3 + 1)\)
(This option correctly shows the first step of substituting the zero powers, resulting in \(-4 (3 + 1)\), before moving to further calculations.)
Based on this analysis, option **d** is the correct choice as it shows proper substitution.
While none of the options correctly conclude the entire expression calculation, only **d** maintains the correct process by generating the equivalent expression.
1. **Evaluate \(12^0\)**:
\[
12^0 = 1
\]
2. **Evaluate \(15^0\)**:
\[
15^0 = 1
\]
Now we can substitute these values back into the original expression:
\[
-4 (3 + 12^0) + 15^0 = -4 (3 + 1) + 1
\]
Next, simplify \(3 + 1\):
\[
= -4 (4) + 1
\]
Now, calculate \(-4 \times 4\):
\[
= -16 + 1
\]
Finally, simplify:
\[
-16 + 1 = -15
\]
Now, let's analyze each option given to see which one corresponds to this correct process.
**a.** \(-4 (3 + 12^0) + 15 = -4 (3 + 1) + 1 = -4 \times 4 + 1 = -4 \times 5 = -20\)
(This is incorrect. It states \(-4 \times 5\) instead of \(-4 \times 4\).)
**b.** \(-4 (3 + 12^0) + 15^0 = -4 (15) + 1 = -60 + 1 = -59\)
(This is incorrect. It does not evaluate \(3 + 1\) correctly.)
**c.** \(-4 (3 + 12^0) + 15^0 = -4 (15) + 15 = -60 + 15 = -45\)
(This is incorrect as it also does not evaluate \(3 + 1\) correctly.)
**d.** \(-4 (3 + 12^0) + 15^0 = -4 (3 + 1)\)
(This option correctly shows the first step of substituting the zero powers, resulting in \(-4 (3 + 1)\), before moving to further calculations.)
Based on this analysis, option **d** is the correct choice as it shows proper substitution.
While none of the options correctly conclude the entire expression calculation, only **d** maintains the correct process by generating the equivalent expression.
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