Use the properties of integer exponents to simplify the expression (−4a4)(−2a2) .(1 point) Responses

Question

8a2
−8a6
8a8
8a6

Answer 1

To simplify the expression \((−4a^4)(−2a^2)\), we can follow these steps:

1. Multiply the coefficients: \(-4 \times -2 = 8\).

2. Multiply the variables using the property of exponents: \(a^4 \times a^2 = a^{4+2} = a^6\).

Now we can combine these results:

\[ (−4a^4)(−2a^2) = 8a^6 \]

Therefore, the simplified expression is \(8a^6\).

So the correct response is 8a6.

Answer 2

are you sure

Answer 3

Yes, I am sure. Let's go through the simplification process step by step again to confirm:

1. Start with the expression: \((−4a^4)(−2a^2)\).

2. Multiply the coefficients:

   • The coefficients are \(-4\) and \(-2\).
   • \(-4 \times -2 = 8\) (the product of two negative numbers is positive).

3. Multiply the variable parts:

   • The variable parts are \(a^4\) and \(a^2\).
   • By using the property of exponents, \(a^4 \times a^2 = a^{4+2} = a^6\).

4. Combine the results:

   • Putting it all together, we have \(8a^6\).

Thus, the simplified expression is indeed \(8a^6\).

So the answer is 8a6. Thank you for your patience!

Answer 4

are you sure double check

Answer 5

Let's double-check the simplification step by step:

Starting with the expression:

\[ (−4a^4)(−2a^2) \]

Step 1: Multiply the coefficients

• The coefficients are \(-4\) and \(-2\).
• \(-4 \cdot -2 = 8\).

Step 2: Multiply the variable parts

• The variable parts are \(a^4\) and \(a^2\).
• Using the property of exponents, when multiplying like bases, we add the exponents: \[ a^4 \cdot a^2 = a^{4 + 2} = a^6. \]

Step 3: Combine the results

Putting the results from Step 1 and Step 2 together: \[ (−4a^4)(−2a^2) = 8a^6. \]

Therefore, the final simplified expression is indeed \(8a^6\).

Thank you for asking me to double-check, and I'm confident that the answer is correct: 8a6.