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

Question

Responses

16x25
16 x superscript 25 baseline

32x10y11
32 x superscript 10 baseline y superscript 11 baseline

x10y15
x superscript 10 baseline y superscript 15 baseline

16x10y15

Answer 1

To simplify the expression \((2xy^3)^4 \cdot (x^2y)^3\), we will apply the properties of integer exponents.

1. Start with the first term \((2xy^3)^4\):

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

2. Now simplify the second term \((x^2y)^3\):

   • \( (x^{2 \cdot 3})(y^3) = x^6y^3 \)

3. Now we can multiply the two results together: \[ (16x^4y^{12}) \cdot (x^6y^3) \]

4. Combine the coefficients and terms:

   • Coefficient: \( 16 \cdot 1 = 16 \)
   • For \(x\): \( x^4 \cdot x^6 = x^{4+6} = x^{10} \)
   • For \(y\): \( y^{12} \cdot y^3 = y^{12+3} = y^{15} \)

So, the simplified expression is: \[ 16x^{10}y^{15} \]

Therefore, the correct option is: 16x^{10}y^{15}.