which of the following is developed to result in the answer of 1?

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. \((-2.97)^0\).

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

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. \(-3^0 + 4.5 = -1 \times 3^0 + 4.5 = -1 \times 1 + 4.5 = -1 + 4.5 = 3.5\).

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

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.

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

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: \( \frac{1}{2} (9 - 1) + 1 \).

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)

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.