Question

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

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