Apply the properties of integer exponents to simplify the algebraic expression (2xy3)4⋅(x2y)3.(1 point) Responses 32x10y11 32 x superscript 10 baseline y superscript 11 baseline 16x10y15 16 x superscript 10 baseline y superscript 15 baseline 16x25 16 x superscript 25 baseline x10y15

Answer 1

To simplify the expression \((2xy^3)^4 \cdot (x^2y)^3\) using the properties of integer exponents, we can follow these steps:

1. Apply the power of a product property \((ab)^n = a^n b^n\):

   • \((2xy^3)^4 = 2^4 \cdot x^4 \cdot (y^3)^4 = 16x^4y^{12}\)
   • \((x^2y)^3 = (x^2)^3 \cdot y^3 = x^6 \cdot y^3\)

2. Multiply the results together:

   • \(16x^4y^{12} \cdot x^6y^3\)

3. Combine like terms (using the property that \(a^m \cdot a^n = a^{m+n}\)):

   • The \(x\) terms: \(x^4 \cdot x^6 = x^{4+6} = x^{10}\)
   • The \(y\) terms: \(y^{12} \cdot y^3 = y^{12+3} = y^{15}\)

4. Putting it all together:

   • The expression becomes \(16 \cdot x^{10} \cdot y^{15} = 16x^{10}y^{15}\).

Therefore, the simplified expression is:

16x^{10}y^{15}