simplify the expression: -5^3√625

Answer 1

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 \(\boxed{-3125}\).

Answer 2

Why do you that answer, explain your reason

Answer 3

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.

Answer 4

write it normal. Please don't put special characters or slashes

Answer 5

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.

Answer 6

why Is 7√625 = 175

Answer 7

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.

Answer 8

please don't put slashes or special characters!! not allowed!

Answer 9

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.

Answer 10

Simplify the expression: 2^√16. And why do you think that's the answer... Remember, NO SPECIAL CHARACTERS OR SLASHES ALLOWED!

Answer 11

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.