Apply the properties of integer exponents to simplify the algebraic expression (2xy^3)^4*(x^2y)^3

Answer 1

To simplify the algebraic expression (2xy^3)^4 * (x^2y)^3 using the properties of integer exponents, we can first apply the power of a power property, which states that (a^m)^n = a^(m*n).

So, for the expression (2xy^3)^4, we raise each component of the base (2, x, and y^3) to the power of 4:

(2xy^3)^4 = (2^4 * x^4 * (y^3)^4)

This simplifies to:

16x^4y^12

Next, we apply the same property to the expression (x^2y)^3:

(x^2y)^3 = (x^2)^3 * y^3

This simplifies to:

x^6y^3

Finally, we multiply the two simplified expressions together:

(16x^4y^12) * (x^6y^3) = 16x^4y^12 * x^6y^3

To multiply the variables, we add their exponents:

16 * x^(4+6) * y^(12+3) = 16x^10y^15

So, the simplified version of the algebraic expression (2xy^3)^4 * (x^2y)^3 is 16x^10y^15.