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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

7 answers

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.

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

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.

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

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.

numbers but no symbols

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!