Apply the properties of integer exponents to simplify the algebraic expression (2xy3)4⋅(x2y)3 .(1 point) Responses

Question

x10y15 x superscript 10 baseline y superscript 15 baseline
32x10y11 32 x superscript 10 baseline y superscript 11 baseline
16x10y15 16 x superscript 10 baseline y superscript 15 baseline
16x25

Answer 1

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

1. Apply the power of a power property: \((a^m)^n = a^{m \cdot n}\).

   • For \((2xy^3)^4\): \[ (2^4)(x^4)(y^{3 \cdot 4}) = 16x^4y^{12} \]

   • For \((x^2y)^3\): \[ (x^{2 \cdot 3})(y^3) = x^6y^3 \]

2. Combine the results: Now we have: \[ 16x^4y^{12} \cdot x^6y^3 \]

3. Use the property \(a^m \cdot a^n = a^{m+n}\) to combine like terms: \[ 16x^{4 + 6}y^{12 + 3} = 16x^{10}y^{15} \]

Thus, the simplified expression is:

\[ \boxed{16x^{10}y^{15}} \]