Question
Simplify the expression: 500x53 Responses 5x24x3 5 x squared cube root of 4 x 5x100x23 5 x cube root of 100 x squared 10x25x 10 x squared square root of 5 x
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Answered by
GPT-4o mini
To simplify the expression you've provided, we need to break down each part carefully.
The expression seems to be a long string of numbers and variables without clear separation. I'll separate it into parts for clarity and then simplify each part.
1. **500 x 53 Responses**
- This could be read as \( 500 \times 53 \).
2. **5 x 24 x 3**
- This could be calculated as \( 5 \times 24 \times 3 \).
3. **5 x squared cube root of 4**
- This seems to be written as \( 5 x^2 \sqrt[3]{4} \).
4. **5 x 100 x 23**
- This appears to be \( 5 \times 100 \times 23 \).
5. **5 x cube root of 100 x squared**
- This could be simplified as \( 5 \sqrt[3]{100} x^2 \).
6. **10 x 25 x 10 x squared square root of 5 x**
- This seems to be \( 10 \times 25 \times 10 x^2 \sqrt{5x} \).
Let’s handle each calculation step-by-step.
### 1. \( 500 \times 53 \)
\[ 500 \times 53 = 26500 \]
### 2. \( 5 \times 24 \times 3 \)
\[ 5 \times 24 = 120 \]
\[ 120 \times 3 = 360 \]
### 3. \( 5 x^2 \sqrt[3]{4} \)
This cannot be simplified further without a numerical value for \( x \):
\[ 5 x^2 \sqrt[3]{4} \]
### 4. \( 5 \times 100 \times 23 \)
\[ 5 \times 100 = 500 \]
\[ 500 \times 23 = 11500 \]
### 5. \( 5 \sqrt[3]{100} x^2 \)
The cube root of 100 can be simplified, but it remains under a root:
\[ 5 \sqrt[3]{100} x^2 \]
Since \( \sqrt[3]{100} = 10^{2/3} \), this remains unchanged unless we need it in decimal.
### 6. \( 10 \times 25 \times 10 x^2 \sqrt{5x} \)
Calculating:
\[ 10 \times 25 = 250 \]
\[ 250 \times 10 = 2500 \]
So we have:
\[ 2500 x^2 \sqrt{5x} \]
### Putting it together
Now, we combine all the results. However, since they are not like terms with respect to base variables, we list them separately:
1. \( 26500 \)
2. \( 360 \)
3. \( 5 x^2 \sqrt[3]{4} \)
4. \( 11500 \)
5. \( 5 \sqrt[3]{100} x^2 \)
6. \( 2500 x^2 \sqrt{5x} \)
The final expression, combining everything, looks as follows:
\[
26500 + 360 + 5 x^2 \sqrt[3]{4} + 11500 + 5 \sqrt[3]{100} x^2 + 2500 x^2 \sqrt{5x}
\]
This is the simplified form of the expression. Without specific values for \( x \), we cannot combine the variable terms further.
The expression seems to be a long string of numbers and variables without clear separation. I'll separate it into parts for clarity and then simplify each part.
1. **500 x 53 Responses**
- This could be read as \( 500 \times 53 \).
2. **5 x 24 x 3**
- This could be calculated as \( 5 \times 24 \times 3 \).
3. **5 x squared cube root of 4**
- This seems to be written as \( 5 x^2 \sqrt[3]{4} \).
4. **5 x 100 x 23**
- This appears to be \( 5 \times 100 \times 23 \).
5. **5 x cube root of 100 x squared**
- This could be simplified as \( 5 \sqrt[3]{100} x^2 \).
6. **10 x 25 x 10 x squared square root of 5 x**
- This seems to be \( 10 \times 25 \times 10 x^2 \sqrt{5x} \).
Let’s handle each calculation step-by-step.
### 1. \( 500 \times 53 \)
\[ 500 \times 53 = 26500 \]
### 2. \( 5 \times 24 \times 3 \)
\[ 5 \times 24 = 120 \]
\[ 120 \times 3 = 360 \]
### 3. \( 5 x^2 \sqrt[3]{4} \)
This cannot be simplified further without a numerical value for \( x \):
\[ 5 x^2 \sqrt[3]{4} \]
### 4. \( 5 \times 100 \times 23 \)
\[ 5 \times 100 = 500 \]
\[ 500 \times 23 = 11500 \]
### 5. \( 5 \sqrt[3]{100} x^2 \)
The cube root of 100 can be simplified, but it remains under a root:
\[ 5 \sqrt[3]{100} x^2 \]
Since \( \sqrt[3]{100} = 10^{2/3} \), this remains unchanged unless we need it in decimal.
### 6. \( 10 \times 25 \times 10 x^2 \sqrt{5x} \)
Calculating:
\[ 10 \times 25 = 250 \]
\[ 250 \times 10 = 2500 \]
So we have:
\[ 2500 x^2 \sqrt{5x} \]
### Putting it together
Now, we combine all the results. However, since they are not like terms with respect to base variables, we list them separately:
1. \( 26500 \)
2. \( 360 \)
3. \( 5 x^2 \sqrt[3]{4} \)
4. \( 11500 \)
5. \( 5 \sqrt[3]{100} x^2 \)
6. \( 2500 x^2 \sqrt{5x} \)
The final expression, combining everything, looks as follows:
\[
26500 + 360 + 5 x^2 \sqrt[3]{4} + 11500 + 5 \sqrt[3]{100} x^2 + 2500 x^2 \sqrt{5x}
\]
This is the simplified form of the expression. Without specific values for \( x \), we cannot combine the variable terms further.
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