Question

Apply the properties of integer exponents to simplify the algebraic expression, which is in parentheses 2XY small three on top outside of the parentheses there’s a small floor times and parentheses X with a small two on top and then why outside of the parentheses there’s a small tree on top. What the answer be X small 10 on top small 15 on top or would it be 16 X small 25 on top or 32X small 10 on top or Y with a small 11 on top or 16 X with a small tan on top with a small 15 on top?

Answer 1

Let's clarify and simplify the given expression step by step using the properties of integer exponents.

The expression you've described can be interpreted as:

\[
(2XY^3)^{4} \cdot (X^2Y)^{3}
\]

Let's break this down:

1. **Expand \( (2XY^3)^{4} \)**:
- \( 2^{4} \)
- \( X^{4} \)
- \( (Y^3)^{4} = Y^{12} \)

Therefore, we have:
\[
(2XY^3)^{4} = 16 X^{4} Y^{12}
\]

2. **Expand \( (X^2Y)^{3} \)**:
- \( (X^2)^{3} = X^{6} \)
- \( (Y)^{3} = Y^{3} \)

Therefore, we have:
\[
(X^2Y)^{3} = X^{6} Y^{3}
\]

3. **Combine the two parts**:
Now we need to multiply the results:
\[
(16 X^{4} Y^{12}) \cdot (X^{6} Y^{3})
\]

The multiplication of the coefficients and the exponents gives:
- Coefficients: \( 16 \)
- For \( X \): \( X^{4} \cdot X^{6} = X^{4+6} = X^{10} \)
- For \( Y \): \( Y^{12} \cdot Y^{3} = Y^{12+3} = Y^{15} \)

Putting it all together, we have:
\[
16 X^{10} Y^{15}
\]

Thus, the simplified expression is:

\[
16 X^{10} Y^{15}
\]

From the options provided, the correct choice is:

**16 X small 10 on top small 15 on top**.