Apply the properties of integer exponents to simplify the algebraic expression (2xy^3)^4*(x^2y)^3
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.
To simplify the algebraic expression (2xy^3)^4 * (x^2y)^3, we can apply the properties of integer exponents.
First, let's simplify (2xy^3)^4 using the property (a*b)^n = a^n * b^n:
(2xy^3)^4 = (2^4) * (x^4) * (y^12) = 16x^4y^12
Next, let's simplify (x^2y)^3 using the property (a^n)^m = a^(n*m):
(x^2y)^3 = x^(2*3) * y^(1*3) = x^6y^3
Now, we can multiply the two simplified expressions:
16x^4y^12 * x^6y^3 = 16x^(4+6) * y^(12+3) = 16x^10 * y^15
Therefore, the simplified form of the expression (2xy^3)^4 * (x^2y)^3 is 16x^10y^15.