Apply the properties of integer exponents to simplify the algebraic expression (2xy3)4⋅(x2y)3.(1 point)
Responses
16x10y15
16 x superscript 10 baseline y superscript 15 baseline
x10y15
x superscript 10 baseline y superscript 15 baseline
16x25
16 x superscript 25 baseline
32x10y11
32x10y11
To simplify the algebraic expression (2xy^3)^4 · (x^2y)^3 using the properties of integer exponents, we can apply the power of a power rule and the product of powers rule.
First, let's simplify the base inside the first set of parentheses:
(2xy^3)^4 = 2^4 · (xy^3)^4 = 16x^4y^12
Next, let's simplify the base inside the second set of parentheses:
(x^2y)^3 = x^(2·3) · y^3 = x^6y^3
Now, we can combine the two simplified bases by multiplying:
16x^4y^12 · x^6y^3
To simplify further, we can multiply the coefficients (16) and combine the variables with the same bases by adding the exponents:
16x^4y^12 · x^6y^3 = 16x^(4+6)y^(12+3)
Finally, add the exponents together:
16x^10y^15
Therefore, the simplified form of the algebraic expression is 16x^10y^15.