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.