Asked by ...hi....
What is the value of 6.9−20?(1 point)Responses4.94.96.96.97.97.95.9
Answers
Answered by
...hi....
Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)0+32(8−270) .(2 points)9⋅(−33)0+32(8−270) = ⋅ +32( – )
Answered by
...hi....
Solve the expression 15⋅805+4(70−6) .(1 point)15⋅805+4(70−6)=
Answered by
...hi....
Use the Power Rule of Exponents to simplify (103)6 .(1 point)
Answered by
...hi....
f the expression 715 was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?(1 point)Responses(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis(718)3left parenthesis 7 superscript 18 baseline right parenthesis cubed(710)5left parenthesis 7 superscript 10 baseline right parenthesis superscript 5 baseline(7⋅7⋅7⋅7⋅7)10
Answered by
...hi....
Use the Power Rule of Exponents to create a simplified equivalent expression for (194)9 .(1 point)
Answered by
GPT-4o mini
To calculate \( 6.9 - 20 \):
\[
6.9 - 20 = -13.1
\]
It appears none of the provided response options include -13.1. Could you please check the options again?
\[
6.9 - 20 = -13.1
\]
It appears none of the provided response options include -13.1. Could you please check the options again?
Answered by
GPT-4o mini
According to the Zero Power Rule, any non-zero number raised to the power of 0 is equal to 1. This can be applied to the term \((-33)^0\).
Let's simplify the expression step by step:
1. Identify the term:
\[
(-33)^0
\]
According to the Zero Power Rule:
\[
(-33)^0 = 1
\]
2. Replace the term:
\[
9 \cdot (-33)^0 + 32(8 - 270)
\]
becomes:
\[
9 \cdot 1 + 32(8 - 270)
\]
3. Thus, the expression simplifies to:
\[
9 + 32(8 - 270)
\]
In conclusion, the equivalent expression is:
\[
9 + 32(8 - 270)
\]
You can further evaluate or simplify \(32(8 - 270)\) if required. The simplified expression you provided is:
\[
9 \cdot 1 + 32(8 - 270)
\] or
\[
9 + 32(8 - 270)
\]
Feel free to ask if you need further assistance!
Let's simplify the expression step by step:
1. Identify the term:
\[
(-33)^0
\]
According to the Zero Power Rule:
\[
(-33)^0 = 1
\]
2. Replace the term:
\[
9 \cdot (-33)^0 + 32(8 - 270)
\]
becomes:
\[
9 \cdot 1 + 32(8 - 270)
\]
3. Thus, the expression simplifies to:
\[
9 + 32(8 - 270)
\]
In conclusion, the equivalent expression is:
\[
9 + 32(8 - 270)
\]
You can further evaluate or simplify \(32(8 - 270)\) if required. The simplified expression you provided is:
\[
9 \cdot 1 + 32(8 - 270)
\] or
\[
9 + 32(8 - 270)
\]
Feel free to ask if you need further assistance!
Answered by
GPT-4o mini
Let's solve the expression step by step:
The given expression is:
\[
15 \cdot 805 + 4(70 - 6)
\]
1. **Calculate \(70 - 6\)**:
\[
70 - 6 = 64
\]
2. **Substitute back into the expression**:
\[
15 \cdot 805 + 4(64)
\]
3. **Calculate \(4 \cdot 64\)**:
\[
4 \cdot 64 = 256
\]
4. **Now the expression is**:
\[
15 \cdot 805 + 256
\]
5. **Calculate \(15 \cdot 805\)**:
\[
15 \cdot 805 = 12075
\]
6. **Finally, add the two results together**:
\[
12075 + 256 = 12331
\]
Therefore, the value of \(15 \cdot 805 + 4(70 - 6)\) is:
\[
\boxed{12331}
\]
The given expression is:
\[
15 \cdot 805 + 4(70 - 6)
\]
1. **Calculate \(70 - 6\)**:
\[
70 - 6 = 64
\]
2. **Substitute back into the expression**:
\[
15 \cdot 805 + 4(64)
\]
3. **Calculate \(4 \cdot 64\)**:
\[
4 \cdot 64 = 256
\]
4. **Now the expression is**:
\[
15 \cdot 805 + 256
\]
5. **Calculate \(15 \cdot 805\)**:
\[
15 \cdot 805 = 12075
\]
6. **Finally, add the two results together**:
\[
12075 + 256 = 12331
\]
Therefore, the value of \(15 \cdot 805 + 4(70 - 6)\) is:
\[
\boxed{12331}
\]
Answered by
GPT-4o mini
The Power Rule of Exponents states that \((a^m)^n = a^{m \cdot n}\).
Given the expression \((10^3)^6\), we can apply the Power Rule as follows:
\[
(10^3)^6 = 10^{3 \cdot 6} = 10^{18}
\]
Thus, the simplified form of \((10^3)^6\) is:
\[
\boxed{10^{18}}
\]
Given the expression \((10^3)^6\), we can apply the Power Rule as follows:
\[
(10^3)^6 = 10^{3 \cdot 6} = 10^{18}
\]
Thus, the simplified form of \((10^3)^6\) is:
\[
\boxed{10^{18}}
\]
Answered by
GPT-4o mini
To simplify \( 7^{15} \) using the Power Rule of Exponents, we need to identify an equivalent expression in expanded form.
The expression \( 7^{15} \) means \( 7 \) multiplied by itself 15 times. So we can write it as:
\[
7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7
\]
Now let's review the answer choices you provided:
1. **(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)**
This is equivalent to \( (7^3)^5 = 7^{15} \), since \( 7^3 \) repeated 5 times gives 15.
2. **\( (7^{18})^3 \)**
This simplifies to \( 7^{54} \), which is not equivalent to \( 7^{15} \).
3. **\( (7^{10})^5 \)**
This simplifies to \( 7^{50} \), which is not equivalent to \( 7^{15} \).
4. **\( (7⋅7⋅7⋅7⋅7)^{10} \)**
This simplifies to \( 7^{50} \), which is not equivalent to \( 7^{15} \).
The first response is the correct expanded equivalent expression for \( 7^{15} \):
\[
(7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7)
\]
Therefore, the answer is:
\[
\text{(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)}
\]
The expression \( 7^{15} \) means \( 7 \) multiplied by itself 15 times. So we can write it as:
\[
7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7
\]
Now let's review the answer choices you provided:
1. **(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)**
This is equivalent to \( (7^3)^5 = 7^{15} \), since \( 7^3 \) repeated 5 times gives 15.
2. **\( (7^{18})^3 \)**
This simplifies to \( 7^{54} \), which is not equivalent to \( 7^{15} \).
3. **\( (7^{10})^5 \)**
This simplifies to \( 7^{50} \), which is not equivalent to \( 7^{15} \).
4. **\( (7⋅7⋅7⋅7⋅7)^{10} \)**
This simplifies to \( 7^{50} \), which is not equivalent to \( 7^{15} \).
The first response is the correct expanded equivalent expression for \( 7^{15} \):
\[
(7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7)
\]
Therefore, the answer is:
\[
\text{(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)}
\]
Answered by
GPT-4o mini
To simplify the expression \((19^4)^9\) using the Power Rule of Exponents, we apply the rule which states that \((a^m)^n = a^{m \cdot n}\).
1. Starting with the expression:
\[
(19^4)^9
\]
2. Apply the Power Rule:
\[
(19^4)^9 = 19^{4 \cdot 9}
\]
3. Calculate \(4 \cdot 9\):
\[
4 \cdot 9 = 36
\]
4. Therefore, the simplified equivalent expression is:
\[
19^{36}
\]
Thus, the final answer is:
\[
\boxed{19^{36}}
\]
1. Starting with the expression:
\[
(19^4)^9
\]
2. Apply the Power Rule:
\[
(19^4)^9 = 19^{4 \cdot 9}
\]
3. Calculate \(4 \cdot 9\):
\[
4 \cdot 9 = 36
\]
4. Therefore, the simplified equivalent expression is:
\[
19^{36}
\]
Thus, the final answer is:
\[
\boxed{19^{36}}
\]