Question

Which of the following shows the correct process of solving −30+4.5 ?(1 point) Responses −30+4.5=−3+4.5=1.5 negative 3 superscript 0 baseline plus 4.5 equals negative 3 plus 4.5 equals 1.5 −30+4.5=−1⋅30+4.5=−1⋅1+4.5=−1+4.5=3.5 negative 3 superscript 0 baseline plus 4.5 equals negative 1 times 3 superscript 0 baseline plus 4.5 equals negative 1 dot 1 plus 4.5 equals negative 1 plus 4.5 equals 3.5 −30+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 −30+4.5=(−3)0+4.5=1+4.5=5.5

Answer 1

Let's evaluate the expression \(-30 + 4.5\).

To solve \(-30 + 4.5\):

1. We start at \(-30\).
2. Adding \(4.5\) means we move \(4.5\) units towards \(0\) (the positive side of the number line).
3. Hence, \(-30 + 4.5 = -25.5\).

Now, examining the responses provided:

• First Response: \(-30 + 4.5 = -3 + 4.5 = 1.5\) (Incorrect)

• Second Response: \(-30+4.5=−1⋅30+4.5=−1⋅1+4.5=−1+4.5=3.5\) (Incorrect)

• Third Response: \(-30+4.5=−3⋅0+4.5=0+4.5=4.5\) (Incorrect)

• Fourth Response: \(-30+4.5=(−3)0+4.5=1+4.5=5.5\) (Incorrect)

None of the responses shown provides the correct steps to solve \(-30 + 4.5\). The correct solution should be \(-30 + 4.5 = -25.5\).

Answer 2

just pick the options I gave you

Answer 3

Apologies for the misunderstanding. Among the options provided, none of them correctly solve the equation \(-30 + 4.5\). However, if I had to choose the one that comes closest to a typical method of processing, I would focus on the formatting and presentation rather than correctness.

That said, none of the responses yield the correct answer or a valid arithmetic process.

If you're looking for the least incorrect option based on common conventions, I can't pick one since all seem incorrect in their calculations.

If you are required to choose despite the errors in all, please select the one that seems most reasonable to you based on procedural resemblance.

Answer 4

Which of the following is an equivalent expression to 7(−5.3)0+4⋅9 when applying the Zero Power Rule? (1 point) Responses 70+4⋅9 Start Fraction 7 over 0 End Fraction plus 4 times 9 71+4⋅9 Start Fraction 7 over 1 End Fraction plus 4 times 9 75.30+36 Start Fraction 7 over 5.3 superscript 0 baseline End Fraction plus 36 75.3+4⋅9

Answer 5

To apply the Zero Power Rule, we need to remember that any non-zero number raised to the power of zero is equal to 1. In the expression \(7(-5.3)^0 + 4 \cdot 9\), we can simplify \((-5.3)^0\) to 1.

Now, let's simplify the expression step by step:

1. Apply the Zero Power Rule:
   \((-5.3)^0 = 1\)

2. Substituting this back into the expression:
   \(7 \cdot 1 + 4 \cdot 9\)
   Which simplifies to:
   \(7 + 36\)

So, \(7 + 36\) is equivalent to the original expression.

Now let’s evaluate the provided options:

1. 70 + 4⋅9 (Incorrect, \(7 \cdot 1\) ≠ 70)
2. 71 + 4⋅9 (Incorrect, \(\text{not } 71\))
3. 75.3 + 36 (Incorrect, since we have \(7 + 36\))
4. 75.3 + 4⋅9 (Incorrect)

None of the options are presenting the correct equivalent expression of \(7 + 36\), which sums to 43.

If you were to choose the option that represents an attempt at simplification, you might pick \(71 + 4 \cdot 9\) since it represents a process of calculation, but it's still technically incorrect. However, based on the correct application of the rules, none of these options correctly equate to the outcome of \(7 + 36\).

In conclusion, \(\mathbf{7 + 36}\) is the simplified equivalent but it isn't explicitly listed among the choices.

Answer 6

hich of the following shows the correct process of solving −4(3+120)+150 by generating an equivalent expression using the Zero Power Rule? (1 point) Responses −4(3+120)+150=−4(3+1)+1=−4⋅4+1=−4⋅5=−20 negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 4 times 5 equals negative 20 −4(3+120)+150=−4(3+1)+1=−4⋅4+1=−16+1=−15 negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 16 plus 1 equals negative 15 −4(3+120)+150 =−4(15)+15=−60+15=−45 negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 15 equals negative 60 plus 15 equals negative 45 −4(3+120)+150=−4(15)+1=−60+1=−59

Answer 7

Let's evaluate the expression \(-4(3 + 120) + 150\) and apply the Zero Power Rule correctly.

First, we simplify the original expression:

1. Calculate \(3 + 120\): \[ 3 + 120 = 123 \]

2. Now substitute this value into the expression: \[ -4(123) + 150 \]

3. Calculate \(-4(123)\): \[ -4 \cdot 123 = -492 \]

4. Now, substitute this into the expression: \[ -492 + 150 \]

5. Calculate \(-492 + 150\): \[ -492 + 150 = -342 \]

Now, let's check the options given along with the consideration of using the Zero Power Rule. The Zero Power Rule states that any non-zero number raised to the power of 0 equals 1.

Evaluating the Options:

1. First Option:
   \(-4(3 + 120) + 150 = -4(3 + 1) + 1 = -4 \cdot 4 + 1 = -4 \cdot 5 = -20\)
   (Incorrect, process is invalid)

2. Second Option:
   \(-4(3 + 12^0) + 15^0 = -4(3 + 1) + 1 = -4 \cdot 4 + 1 = -4 \cdot 5 = -20\)
   (Incorrect, process is invalid)

3. Third Option:
   \(-4(3 + 120) + 150 = -4(15) + 15 = -60 + 15 = -45\)
   (Incorrect, original expression misinterpreted)

4. Fourth Option:
   \(-4(3 + 120) + 150 = -4(15) + 1 = -60 + 1 = -59\)
   (Incorrect, original expression misinterpreted)

After evaluation:

• None of the options correctly apply the Zero Power Rule or provide valid calculations to solve the expression \(-4(3 + 120) + 150\) accurately.

However, none of the answers match the correct final solution of \(-342\). Each option contains a significant error in processing the operations or logically applying the Zero Power Rule.

If I had to suggest picking one based on any semblance of correctness in their method (assuming you ignore that they result in wrong final answers), the options that use \(3 + 1\) might note a better format with the Zero Power theorem, but still result in incorrect calculations.

In summary, none of the given answers are correct.

Answer 8

Which expression is correctly developed to use the Power Rule of Exponents?(1 point) Responses (78)⋅(710) left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis (74)8 left parenthesis 7 superscript 4 baseline right parenthesis superscript 8 baseline (−5)0 left parenthesis negative 5 right parenthesis superscript 0 baseline 129

Answer 9

To determine which expression is correctly developed to use the Power Rule of Exponents, we should recall the Power Rule, which states:

\[ (a^m)^n = a^{m \cdot n} \]

Now, let's analyze each of the provided expressions:

1. First Option:
   \((7^8) \cdot (7^{10})\)
   This expression does not explicitly apply the Power Rule, but it utilizes the Property of Exponents that states \(a^m \cdot a^n = a^{m+n}\). Therefore, it is correctly developed but is indicative of the Product of Powers Rule, not the Power Rule.

2. Second Option:
   \((7^4)^8\)
   Here, this is a direct application of the Power Rule where \(7^4\) is raised to the power of 8. According to the Power Rule, this can be simplified to \(7^{4 \cdot 8} = 7^{32}\). Hence, this expression correctly uses the Power Rule of exponents.

3. Third Option:
   \((-5)^0\)
   Any non-zero number raised to the power of 0 equals 1, but this expression does not showcase the development of the Power Rule of Exponents.

4. Fourth Option:
   \(1^{29}\)
   This expression states that 1 raised to any power is still 1, but again, it does not demonstrate the application of the Power Rule.

Conclusion:

The expression that is correctly developed to use the Power Rule of Exponents is:

\[ \text{(74)}^8 \quad \text{(which is equivalent to (7^4)^8)} \]

Thus, the correct answer is the second option: \((7^4)^8\)

Answer 10

Which of the following correctly used the Power Rule of Exponents in the expression (109)7 ?(1 point) Responses 907 90 superscript 7 baseline 1063 10 superscript 63 baseline 102 10 superscript 2 baseline 1016

Answer 11

To determine which response correctly uses the Power Rule of Exponents on the expression \((10^9)^7\), we will apply the Power Rule, which states:

\[ (a^m)^n = a^{m \cdot n} \]

Applying the Power Rule to \((10^9)^7\):

\[ (10^9)^7 = 10^{9 \cdot 7} = 10^{63} \]

Now let's evaluate the responses based on this calculation:

1. First Option: \(10^7\)
   (Incorrect; this does not apply the Power Rule correctly.)

2. Second Option: \(10^{63}\)
   (Correct; this is the correct application of the Power Rule.)

3. Third Option: \(10^2\)
   (Incorrect; this does not apply the Power Rule correctly.)

4. Fourth Option: \(10^{16}\)
   (Incorrect; this does not apply the Power Rule correctly.)

Conclusion:

The expression that correctly uses the Power Rule of Exponents in the expression \((10^9)^7\) is:

\[ 10^{63} \]

Thus, the correct answer is the second option: \(10^{63}\).