Asked by Cassie E. Acosta
simplify the expression: -5^3√625
Answers
Answered by
Cassie E. Acosta
Why do you that answer, explain your reason
Answered by
Cassie E. Acosta
write it normal. Please don't put special characters or slashes
Answered by
Cassie E. Acosta
why Is 7√625 = 175
Answered by
Cassie E. Acosta
please don't put slashes or special characters!! not allowed!
Answered by
Cassie E. Acosta
Simplify the expression: 2^√16. And why do you think that's the answer... Remember, NO SPECIAL CHARACTERS OR SLASHES ALLOWED!
Answered by
GPT-4o mini
To simplify the expression \(-5^3\sqrt{625}\), we will break it down step by step.
1. **Calculate \(-5^3\)**:
\[
-5^3 = - (5 \times 5 \times 5) = -125
\]
2. **Calculate \(\sqrt{625}\)**:
\[
\sqrt{625} = 25
\]
(since \(25 \times 25 = 625\))
3. **Multiply the results**:
\[
-5^3 \sqrt{625} = -125 \times 25
\]
4. **Calculate \(-125 \times 25\)**:
\[
-125 \times 25 = -3125
\]
Thus, the simplified expression is \(\boxed{-3125}\).
1. **Calculate \(-5^3\)**:
\[
-5^3 = - (5 \times 5 \times 5) = -125
\]
2. **Calculate \(\sqrt{625}\)**:
\[
\sqrt{625} = 25
\]
(since \(25 \times 25 = 625\))
3. **Multiply the results**:
\[
-5^3 \sqrt{625} = -125 \times 25
\]
4. **Calculate \(-125 \times 25\)**:
\[
-125 \times 25 = -3125
\]
Thus, the simplified expression is \(\boxed{-3125}\).
Answered by
GPT-4o mini
Sure! Let's break down the process of simplifying the expression \(-5^3\sqrt{625}\) step by step and explain each part so you can understand the reasoning behind it.
### Step 1: Understand the Expression
The expression consists of two main components:
1. \(-5^3\): This indicates the negative of \(5\) raised to the power of 3.
2. \(\sqrt{625}\): This represents the square root of \(625\).
### Step 2: Calculate \(-5^3\)
- **Exponentiation**: When we see \(5^3\), this means \(5\) multiplied by itself three times:
\[
5^3 = 5 \times 5 \times 5 = 125.
\]
- **Including the negative**: Because of the negative sign in front of \(5^3\), we write:
\[
-5^3 = -125.
\]
### Step 3: Calculate \(\sqrt{625}\)
- **Finding the Square Root**: The square root \(\sqrt{625}\) is asking for a number that, when multiplied by itself, gives \(625\).
- **Identifying the Root**: Since \(25 \times 25 = 625\), we have:
\[
\sqrt{625} = 25.
\]
### Step 4: Combine the Results
Now we have both components:
- \(-5^3\) calculated to \(-125\)
- \(\sqrt{625}\) calculated to \(25\)
### Step 5: Multiply the Two Results
We multiply the two results together:
\[
-125 \times 25.
\]
- **Calculating the Product**:
- First, we'll calculate \(125 \times 25\):
\[
125 \times 25 = 3125.
\]
- Now, applying the negative sign:
\[
-125 \times 25 = -3125.
\]
### Final Result
Putting everything together, the simplified form of the expression \(-5^3\sqrt{625}\) is:
\[
\boxed{-3125}.
\]
### Summary of Reasoning
The steps followed each part of the expression clearly:
- Evaluating the exponent and applying the negative sign.
- Finding the square root of \(625\).
- Finally, multiplying the two results together to get the final answer. Each calculation was methodical and followed basic arithmetic rules, ensuring accuracy.
### Step 1: Understand the Expression
The expression consists of two main components:
1. \(-5^3\): This indicates the negative of \(5\) raised to the power of 3.
2. \(\sqrt{625}\): This represents the square root of \(625\).
### Step 2: Calculate \(-5^3\)
- **Exponentiation**: When we see \(5^3\), this means \(5\) multiplied by itself three times:
\[
5^3 = 5 \times 5 \times 5 = 125.
\]
- **Including the negative**: Because of the negative sign in front of \(5^3\), we write:
\[
-5^3 = -125.
\]
### Step 3: Calculate \(\sqrt{625}\)
- **Finding the Square Root**: The square root \(\sqrt{625}\) is asking for a number that, when multiplied by itself, gives \(625\).
- **Identifying the Root**: Since \(25 \times 25 = 625\), we have:
\[
\sqrt{625} = 25.
\]
### Step 4: Combine the Results
Now we have both components:
- \(-5^3\) calculated to \(-125\)
- \(\sqrt{625}\) calculated to \(25\)
### Step 5: Multiply the Two Results
We multiply the two results together:
\[
-125 \times 25.
\]
- **Calculating the Product**:
- First, we'll calculate \(125 \times 25\):
\[
125 \times 25 = 3125.
\]
- Now, applying the negative sign:
\[
-125 \times 25 = -3125.
\]
### Final Result
Putting everything together, the simplified form of the expression \(-5^3\sqrt{625}\) is:
\[
\boxed{-3125}.
\]
### Summary of Reasoning
The steps followed each part of the expression clearly:
- Evaluating the exponent and applying the negative sign.
- Finding the square root of \(625\).
- Finally, multiplying the two results together to get the final answer. Each calculation was methodical and followed basic arithmetic rules, ensuring accuracy.
Answered by
GPT-4o mini
Sure! Let's simplify the expression negative five cubed times the square root of six hundred twenty-five step by step.
### Step 1: Understand the Expression
The expression consists of two parts:
1. Negative five cubed: This means the negative of five raised to the power of three.
2. The square root of six hundred twenty-five: This represents the number that, when multiplied by itself, gives six hundred twenty-five.
### Step 2: Calculate Negative Five Cubed
When we see five cubed, it means five multiplied by itself three times:
Five cubed equals five times five times five, which is one hundred twenty-five.
Since there is a negative sign, we need to write:
Negative five cubed equals negative one hundred twenty-five.
### Step 3: Calculate the Square Root of Six Hundred Twenty-Five
The square root of six hundred twenty-five asks for a number that, when multiplied by itself, equals six hundred twenty-five.
The number that fulfills this is twenty-five because twenty-five times twenty-five equals six hundred twenty-five.
### Step 4: Combine the Results
Now we have both parts:
Negative five cubed is negative one hundred twenty-five.
The square root of six hundred twenty-five is twenty-five.
### Step 5: Multiply the Two Results
We will now multiply the two results together:
Negative one hundred twenty-five multiplied by twenty-five.
Calculating one hundred twenty-five times twenty-five gives us three thousand one hundred twenty-five.
Applying the negative sign gives us:
Negative one hundred twenty-five times twenty-five equals negative three thousand one hundred twenty-five.
### Final Result
So, the simplified result of the expression negative five cubed times the square root of six hundred twenty-five is negative three thousand one hundred twenty-five.
### Step 1: Understand the Expression
The expression consists of two parts:
1. Negative five cubed: This means the negative of five raised to the power of three.
2. The square root of six hundred twenty-five: This represents the number that, when multiplied by itself, gives six hundred twenty-five.
### Step 2: Calculate Negative Five Cubed
When we see five cubed, it means five multiplied by itself three times:
Five cubed equals five times five times five, which is one hundred twenty-five.
Since there is a negative sign, we need to write:
Negative five cubed equals negative one hundred twenty-five.
### Step 3: Calculate the Square Root of Six Hundred Twenty-Five
The square root of six hundred twenty-five asks for a number that, when multiplied by itself, equals six hundred twenty-five.
The number that fulfills this is twenty-five because twenty-five times twenty-five equals six hundred twenty-five.
### Step 4: Combine the Results
Now we have both parts:
Negative five cubed is negative one hundred twenty-five.
The square root of six hundred twenty-five is twenty-five.
### Step 5: Multiply the Two Results
We will now multiply the two results together:
Negative one hundred twenty-five multiplied by twenty-five.
Calculating one hundred twenty-five times twenty-five gives us three thousand one hundred twenty-five.
Applying the negative sign gives us:
Negative one hundred twenty-five times twenty-five equals negative three thousand one hundred twenty-five.
### Final Result
So, the simplified result of the expression negative five cubed times the square root of six hundred twenty-five is negative three thousand one hundred twenty-five.
Answered by
GPT-4o mini
To understand why \( 7\sqrt{625} = 175 \), let's break it down step by step.
### Step 1: Calculate the Square Root of 625
First, we need to find \( \sqrt{625} \). The square root of a number is the value that, when multiplied by itself, gives that number.
- The number \( 25 \times 25 \) equals \( 625 \).
- Therefore, \( \sqrt{625} = 25 \).
### Step 2: Calculate \( 7 \times \sqrt{625} \)
Now that we know \( \sqrt{625} = 25 \), we can substitute that back into the expression:
\[
7\sqrt{625} = 7 \times 25
\]
### Step 3: Multiply 7 by 25
Next, we calculate \( 7 \times 25 \):
\[
7 \times 25 = 175
\]
### Conclusion
So, combining all the steps, we see that:
\[
7\sqrt{625} = 7 \times 25 = 175
\]
Thus, \( 7\sqrt{625} = 175 \) is correct.
### Step 1: Calculate the Square Root of 625
First, we need to find \( \sqrt{625} \). The square root of a number is the value that, when multiplied by itself, gives that number.
- The number \( 25 \times 25 \) equals \( 625 \).
- Therefore, \( \sqrt{625} = 25 \).
### Step 2: Calculate \( 7 \times \sqrt{625} \)
Now that we know \( \sqrt{625} = 25 \), we can substitute that back into the expression:
\[
7\sqrt{625} = 7 \times 25
\]
### Step 3: Multiply 7 by 25
Next, we calculate \( 7 \times 25 \):
\[
7 \times 25 = 175
\]
### Conclusion
So, combining all the steps, we see that:
\[
7\sqrt{625} = 7 \times 25 = 175
\]
Thus, \( 7\sqrt{625} = 175 \) is correct.
Answered by
GPT-4o mini
I apologize for that oversight. Let me explain without using slashes or special characters.
To understand why seven times the square root of six hundred twenty-five equals one hundred seventy-five, let's break it down step by step.
**Step 1: Calculate the Square Root of Six Hundred Twenty-Five**
First, we find the square root of six hundred twenty-five. The square root of a number is the value that, when multiplied by itself, gives that number.
The number twenty-five multiplied by twenty-five equals six hundred twenty-five. Therefore, the square root of six hundred twenty-five is twenty-five.
**Step 2: Multiply Seven by the Square Root of Six Hundred Twenty-Five**
Now that we know the square root of six hundred twenty-five is twenty-five, we can substitute that into our expression.
This means we have seven multiplied by twenty-five.
**Step 3: Calculate Seven Times Twenty-Five**
Next, we multiply seven by twenty-five. Doing this calculation gives us one hundred seventy-five.
**Conclusion**
Putting it all together, we find that seven times the square root of six hundred twenty-five equals one hundred seventy-five.
To understand why seven times the square root of six hundred twenty-five equals one hundred seventy-five, let's break it down step by step.
**Step 1: Calculate the Square Root of Six Hundred Twenty-Five**
First, we find the square root of six hundred twenty-five. The square root of a number is the value that, when multiplied by itself, gives that number.
The number twenty-five multiplied by twenty-five equals six hundred twenty-five. Therefore, the square root of six hundred twenty-five is twenty-five.
**Step 2: Multiply Seven by the Square Root of Six Hundred Twenty-Five**
Now that we know the square root of six hundred twenty-five is twenty-five, we can substitute that into our expression.
This means we have seven multiplied by twenty-five.
**Step 3: Calculate Seven Times Twenty-Five**
Next, we multiply seven by twenty-five. Doing this calculation gives us one hundred seventy-five.
**Conclusion**
Putting it all together, we find that seven times the square root of six hundred twenty-five equals one hundred seventy-five.
Answered by
GPT-4o mini
To simplify the expression two raised to the square root of sixteen, let's break it down step by step.
**Step 1: Calculate the Square Root of Sixteen**
First, we need to find the square root of sixteen. The square root of a number is the value that, when multiplied by itself, results in that number.
In this case, four multiplied by four equals sixteen. So, the square root of sixteen is four.
**Step 2: Substitute the Square Root Back into the Expression**
Now, we take the square root we just calculated and replace it in the original expression. This means two raised to the square root of sixteen becomes two raised to the power of four.
**Step 3: Calculate Two Raised to the Power of Four**
Now we calculate two raised to the power of four. This means multiplying two by itself four times:
Two multiplied by two is four. Then, four multiplied by two is eight. Finally, eight multiplied by two is sixteen.
So, two raised to the power of four equals sixteen.
**Conclusion**
Therefore, the simplified expression for two raised to the square root of sixteen is sixteen.
The reasoning is that we first calculated the square root and then evaluated the exponentiation to arrive at the final answer.
**Step 1: Calculate the Square Root of Sixteen**
First, we need to find the square root of sixteen. The square root of a number is the value that, when multiplied by itself, results in that number.
In this case, four multiplied by four equals sixteen. So, the square root of sixteen is four.
**Step 2: Substitute the Square Root Back into the Expression**
Now, we take the square root we just calculated and replace it in the original expression. This means two raised to the square root of sixteen becomes two raised to the power of four.
**Step 3: Calculate Two Raised to the Power of Four**
Now we calculate two raised to the power of four. This means multiplying two by itself four times:
Two multiplied by two is four. Then, four multiplied by two is eight. Finally, eight multiplied by two is sixteen.
So, two raised to the power of four equals sixteen.
**Conclusion**
Therefore, the simplified expression for two raised to the square root of sixteen is sixteen.
The reasoning is that we first calculated the square root and then evaluated the exponentiation to arrive at the final answer.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.