Question

Which of the following shows the correct process of solving −3^0+4.5 ?
Responses

−3^0+4.5=−3⋅0+4.5=0+4.5=4.5
negative 3 superscript 0 baseline plus 4.5 equals negative 3 times 0 plus 4.5 equals 0 plus 4.5 equals 4.5

−3^0+4.5=−3+4.5=1.5
negative 3 superscript 0 baseline plus 4.5 equals negative 3 plus 4.5 equals 1.5

−3^0+4.5=(−3)^0+4.5=1+4.5=5.5
negative 3 superscript 0 baseline plus 4.5 equals left parenthesis negative 3 right parenthesis superscript 0 baseline plus 4.5 equals 1 plus 4.5 equals 5.5

−3^0+4.5=−1⋅3^0+4.5=−1⋅1+4.5=−1+4.5=3.5

Answer 1

Which of the following is an equivalent expression to 7/(−5.3)^0+4⋅9 when applying the Zero Power Rule?
Responses

7/5.3+4⋅9
Start Fraction 7 over 5.3 End Fraction plus 4 times 9

7/1+4⋅9
Start Fraction 7 over 1 End Fraction plus 4 times 9

7/5.3^0+36
Start Fraction 7 over 5.3 superscript 0 baseline End Fraction plus 36

7/0+4⋅9
Start Fraction 7 over 0 End Fraction plus 4 times 9

Answer 2

Which of the following is an equivalent expression to 1/2(9−7^0)+(−29)^0 ? (1 point)
Responses

1/2(9−1)+1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis plus 1

1/2(9−0)+0
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0

1/2(9−1)−1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1

1/2(2)+1

Answer 3

numbers but no symbols

Answer 4

To solve the expression \(-3^0 + 4.5\), we need to follow the correct order of operations while properly interpreting the expression.

1. **Calculate \(3^0\)**: Any non-zero number raised to the power of 0 is 1. Thus, \(3^0 = 1\).
2. **Then apply the negative sign**: So, \(-3^0 = -1\).
3. **Now substitute back into the expression**:
\(-3^0 + 4.5 = -1 + 4.5\).
4. **Finally, perform the addition**:
\(-1 + 4.5 = 3.5\).

Thus, the correct process and result is:

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

The fourth response correctly represents this process.

Answer 5

To simplify the expression \(7/(-5.3)^0 + 4\cdot9\) using the Zero Power Rule, we first need to apply the rule itself. The Zero Power Rule states that any non-zero number raised to the power of 0 is equal to 1.

In this case:
- \((-5.3)^0 = 1\).

Now we can substitute this in:

\[
7/(-5.3)^0 + 4\cdot9 = 7/1 + 4\cdot9.
\]

Next, calculate \(4 \cdot 9\):

\[
4 \cdot 9 = 36.
\]

So the expression simplifies to:

\[
7/1 + 36.
\]

Thus, the equivalent expression is:

\[
7/1 + 4\cdot9.
\]

The correct response is:

**7/1 + 4⋅9**
Start Fraction 7 over 1 End Fraction plus 4 times 9.

Answer 6

To simplify the expression

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

we first apply the Zero Power Rule.

1. **Calculate \(7^0\)**: Any non-zero number raised to the power of 0 is equal to 1. Thus, \(7^0 = 1\).
2. **Calculate \((-29)^0\)**: Similarly, \((-29)^0 = 1\).

Now we can substitute these values back into the expression:

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

This simplifies to:

\[
\frac{1}{2}(9 - 1) + 1 = \frac{1}{2}(8) + 1 = 4 + 1 = 5.
\]

Now let's look at the answers provided:

1. **\(\frac{1}{2}(9-1) + 1\)**: This simplifies to \(4 + 1 = 5\). (Correct)
2. **\(\frac{1}{2}(9-0) + 0\)**: This simplifies to \(\frac{1}{2}(9) + 0 = 4.5\). (Incorrect)
3. **\(\frac{1}{2}(9-1) - 1\)**: This simplifies to \(4 - 1 = 3\). (Incorrect)
4. **\(\frac{1}{2}(2) + 1\)**: This simplifies to \(1 + 1 = 2\). (Incorrect)

The correct response is:

**\(\frac{1}{2}(9−1) + 1\)**
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis plus 1.

Answer 7

I apologize for the misunderstanding! Here’s the information just with numbers:

The expression simplifies as follows:

1. **Calculate 7^0**: This equals 1.
2. **Calculate (-29)^0**: This also equals 1.

Now substitute back into the expression:

1/2 (9 - 1) + 1

This simplifies to:

1/2 (8) + 1 = 4 + 1 = 5

Among your options, the equivalent expression is:

1/2 (9 - 1) + 1

If you have further questions or need more help, feel free to ask!