(-6a^5b)^2/12a^7b-8a^3b

Answer 1

To simplify the expression \((-6a^5b)^2 / (12a^7b - 8a^3b)\), we will follow the order of operations and simplify each part step by step.

1. Simplify the numerator: \[ (-6a^5b)^2 = (-6)^2 (a^5)^2 (b)^2 = 36a^{10}b^2 \]

2. Simplify the denominator: Combine the terms in the denominator: \[ 12a^7b - 8a^3b = (12a^7 - 8a^3)b = 4a^3(3a^4 - 2)b \]

3. Combine the results: Now, substitute the simplified numerator and denominator: \[ \frac{36a^{10}b^2}{4a^3(3a^4 - 2)b} \]

4. Simplify the fraction: Divide the coefficients and variables:

   • Coefficients: \(\frac{36}{4} = 9\)
   • For \(a\): \(\frac{a^{10}}{a^3} = a^{10-3} = a^7\)
   • For \(b\): \(\frac{b^2}{b} = b^{2-1} = b\)

   Putting it all together: \[ \frac{36a^{10}b^2}{4a^3(3a^4 - 2)b} = \frac{9a^7b}{3a^4 - 2} \]

Thus, the simplified expression is: \[ \frac{9a^7b}{3a^4 - 2} \]

Answer 2

Thus, the simplified expression is:
\[
\frac{9a^7b}{3a^4 - 2}
\]
Please clarify this answer

Answer 3

Certainly! Let’s clarify the solution step by step to ensure everything is accurately presented.

We started with the expression:

\[ \frac{(-6a^5b)^2}{12a^7b - 8a^3b} \]

Step 1: Simplify the numerator

Calculating the square of the numerator: \[ (-6a^5b)^2 = (-6)^2 (a^5)^2 (b)^2 = 36a^{10}b^2 \]

Step 2: Simplify the denominator

Now, we simplify the denominator: \[ 12a^7b - 8a^3b = (12a^7 - 8a^3)b = 4a^3(3a^4 - 2)b \] This means we factored out \(4a^3\) from the expression.

Step 3: Combine the results

Now we substitute the simplified numerator and denominator into the expression: \[ \frac{36a^{10}b^2}{4a^3(3a^4 - 2)b} \]

Step 4: Simplification of the fraction

Now we simplify:

1. Coefficients: \(\frac{36}{4} = 9\)

2. For \(a\): \(\frac{a^{10}}{a^3} = a^{10-3} = a^7\)

3. For \(b\): \(\frac{b^2}{b} = b^{2-1} = b\)

Putting it all together gives us: \[ \frac{36a^{10}b^2}{4a^3(3a^4 - 2)b} = \frac{9a^7b}{3a^4 - 2} \]

Final Answer:

So the simplified expression is: \[ \boxed{\frac{9a^7b}{3a^4 - 2}} \]

This expression is now in its simplest form. If there's any other specific aspect of the solution you'd like clarified or if you have further questions, please let me know!

Answer 4

So the answer is 9a^7b 3a^4-2?

Answer 5

It seems like there might be some confusion regarding the format of the answer. Let's clarify it:

The simplified expression we derived is:

\[ \frac{9a^7b}{3a^4 - 2} \]

This means that \(9a^7b\) is the numerator and \(3a^4 - 2\) is the denominator. The correct way to express it is as a fraction:

\[ \frac{9a^7b}{3a^4 - 2} \]

So, to confirm: the expression is not simply \(9a^7b\) and \(3a^4 - 2\) next to each other. Instead, it is a fraction where \(9a^7b\) is divided by \(3a^4 - 2\).

If you meant to write it more clearly:

\[ \text{Final Answer: } \frac{9a^7b}{3a^4 - 2} \]

Let me know if this clarifies your question!

Answer 6

So I would put (9a^7b) (3a^4-2)

Answer 7

It seems there's still a bit of confusion. Let me clarify how to express the answer correctly.

The final answer we've simplified to is:

\[ \frac{9a^7b}{3a^4 - 2} \]

Here's how this expression should be interpreted and written:

• This expression means \(9a^7b\) is the numerator (the top part of the fraction), and \(3a^4 - 2\) is the denominator (the bottom part of the fraction).

So, if you want to write it as a fraction, you should use the fraction format, not parentheses directly next to each other. Here are a few ways to express it:

As a Fraction:

• With fraction notation: \( \frac{9a^7b}{3a^4 - 2} \)

In a Text Format:

• In plain text: "9a^7b over (3a^4 - 2)" or "9a^7b divided by (3a^4 - 2)"

If your context requires multiplication:

If you were to literally represent it in a multiplication context, that would imply you are multiplying:

\[ (9a^7b) \cdot (3a^4 - 2) \] But this is not what's intended in this scenario; we are dividing \(9a^7b\) by \(3a^4 - 2\).

Conclusion

To summarize, your final answer should be:

\[ \frac{9a^7b}{3a^4 - 2} \]

If you want to state it in any form, please ensure it's clear that \(9a^7b\) is over or divided by \(3a^4 - 2\). Let me know if you need anything else!

Answer 8

So 9a^7b/3a^4-2 is the answer

Answer 9

To clarify:

The simplified expression we arrived at is:

\[ \frac{9a^7b}{3a^4 - 2} \]

This is the correct format for the answer.

If you write it as:

\[ 9a^7b \div (3a^4 - 2) \]

or simply state it as:

• "9a^7b over (3a^4 - 2)"
• "9a^7b divided by (3a^4 - 2)"

Note: Ensure that the denominator \(3a^4 - 2\) is clearly indicated as being in the denominator of the fraction.

Final Answer

So yes, the answer is:

\[ \frac{9a^7b}{3a^4 - 2} \]

Make sure the fraction form is maintained for clarity! If you need further assistance, feel free to ask.