Question

Simplify the expression (4x3)2
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

u sure

Answer 2

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 3

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 4

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 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.