Simplify the expression and parentheses for X power of three outside of the parentheses of power of two using the properties of integer exponents with the answer. Be 8X power at six or 4X power of six or 16 X power of six or 16 X power of five.

Answer 1

To simplify the expression \( (X^3)^2 \) using the properties of exponents, we apply the power of a power property, which states that \( (a^m)^n = a^{m \cdot n} \).

So, we have:

\[ (X^3)^2 = X^{3 \cdot 2} = X^6 \]

At this point, you need to clarify how exactly you want to combine this with the coefficient. However, if you mean to express \( 8X^6 \), \( 4X^6 \), \( 16X^6 \), or \( 16X^5 \) based on some prior context, we can assert that you would end up with \( X^6 \) itself, with any numerical coefficient depending on the context or preceding expressions.

Assuming you have a coefficient of 8, 4, 16, or others, we can summarize:

1. If you have \( 8 \cdot (X^6) \), it simplifies to \( 8X^6 \).
2. If you have \( 4 \cdot (X^6) \), it simplifies to \( 4X^6 \).
3. If you have \( 16 \cdot (X^6) \), it simplifies to \( 16X^6 \).
4. If you have \( 16 \cdot (X^5) \), it simply remains \( 16X^5\).

Thus, the specific simplification would depend on the context you are referring to. The exponent simplification leads to \( X^6 \).