simplify (4xy^2)^3(xy)^5
To simplify (4xy^2)^3(xy)^5, we can use the power of a power property.
(4xy^2)^3(xy)^5 can be written as (4^3 * x^3 * (y^2)^3) * (x^5 * y^5).
This simplifies to 64x^3y^6 * x^5y^5.
Now, we can simplify further by adding the exponents for like terms.
This results in 64x^(3+5)y^(6+5), which simplifies to 64x^8y^11.
Therefore, the simplified form of (4xy^2)^3(xy)^5 is 64x^8y^11.
To simplify the expression (4xy^2)^3(xy)^5, we can apply the exponent rules and perform the necessary operations.
First, let's simplify the expression inside the parentheses, (4xy^2)^3.
(4xy^2)^3 = 4^3 * (x^1)^3 * (y^2)^3
Simplifying further:
= 64 * x^3 * y^6
Now, let's simplify the expression outside the parentheses, (xy)^5.
(xy)^5 = (x^1 * y^1)^5
Using the exponent rule, we can apply the exponent to each term:
= x^(1*5) * y^(1*5)
Simplifying further:
= x^5 * y^5
Now let's combine the two simplified expressions:
= (64 * x^3 * y^6)(x^5 * y^5)
Multiplying the constants:
= 64 * x^3 * y^6 * x^5 * y^5
Combining the variables of the same base (x and y):
= 64 * x^(3+5) * y^(6+5)
Simplifying the exponents:
= 64 * x^8 * y^11
Therefore, the simplified expression is 64x^8y^11.