Simplify the expression (4x3)2

Question

using the properties of integer exponents.(1 point)
Responses

16x6
16 x superscript 6 baseline

4x6
4 x superscript 6 baseline

16x5
16 x superscript 5 baseline

8x6

Answer 1

To simplify the expression \((4x^3)^2\) using the properties of integer exponents, you can apply the power of a product property, which states that \((ab)^n = a^n b^n\) and the power of a power property, which states that \((a^m)^n = a^{m \cdot n}\).

1. Start with the expression: \[ (4x^3)^2 \]

2. Apply the power of a product property: \[ 4^2 \cdot (x^3)^2 \]

3. Calculate \(4^2\) and apply the power of a power property to \(x^3\): \[ 16 \cdot x^{3 \cdot 2} = 16 \cdot x^6 \]

Putting it all together, we have: \[ 16x^6 \]

So the simplified expression is:

16x^6.

Answer 2

u sure

Answer 3

Yes, I am sure. Let's recap the simplification process step-by-step to confirm:

1. We start with the expression: \((4x^3)^2\).

2. According to the properties of exponents (specifically, the power of a product and the power of a power properties), we can break this down as follows: \[ (ab)^n = a^n \cdot b^n \] which means: \[ (4x^3)^2 = 4^2 \cdot (x^3)^2 \]

3. Now, we calculate each part:

   • \(4^2 = 16\)
   • \((x^3)^2 = x^{3 \cdot 2} = x^6\)

4. Putting it all together: \[ (4x^3)^2 = 16 \cdot x^6 = 16x^6 \]

Thus, the final simplified expression is indeed 16x^6. If you have further questions or need assistance with another topic, feel free to ask!

Answer 4

Apply the properties of integer exponents to generate an equivalent algebraic expression to (4x4y−4)3(x7y3)2
.(1 point)
Responses

4x2y18
Start Fraction 4 over x squared y superscript 18 baseline End Fraction

64x20
Start Fraction 64 over x superscript 20 baseline End Fraction

x2y1864
Start Fraction x squared y superscript 18 baseline over 64 End Fraction

64x2y18

Answer 5

To simplify the expression \((4x^4y^{-4})^3(x^7y^3)^2\) using the properties of integer exponents, follow these steps:

1. Simplify each part separately:

   • For \((4x^4y^{-4})^3\): \[ (4^3)(x^{4 \cdot 3})(y^{-4 \cdot 3}) = 64x^{12}y^{-12} \]
   • For \((x^7y^3)^2\): \[ (x^{7 \cdot 2})(y^{3 \cdot 2}) = x^{14}y^6 \]

2. Combine the results: Now, we multiply the two results: \[ (64x^{12}y^{-12})(x^{14}y^6) \] To combine the terms with the same base, we add the exponents:

   • For \(x\): \[ x^{12 + 14} = x^{26} \]
   • For \(y\): \[ y^{-12 + 6} = y^{-6} \]

3. Putting it all together: This gives us: \[ 64x^{26}y^{-6} \]

4. Rewrite y with a positive exponent: To express \(y^{-6}\) in a positive exponent, we can write it as: \[ \frac{64x^{26}}{y^6} \]

Now, looking at the provided responses, the expression simplifies to:

\[ \frac{64x^{26}}{y^6} \]

However, if you want to match it closely with the options given, we simplify further if needed, but none of those answers seem to match with the final simplified expression I got.

Among the options provided, it appears the closest option is not in correct alignment with the final answer.

Please check if additional options need to be evaluated, or if a different interpretation of the question is necessary.