Simplify (4xy2)3(xy)5
A. 64x^8y^11
B. 64x^15y^30
C. 12x^2y^11
D. 12x^8y^11
11 years ago
11 years ago
(4xy^2)^3(xy)^5
4^3 x^3 (y^2)^3 x^5 y^5
64 x^3 y^6 x^5 y^5
64 x^8 y^11
(A)
1 year ago
To simplify the expression (4xy^2)^3(xy)^5, we need to raise each term inside the parentheses to the power outside the parentheses and then multiply the resulting terms together.
First, let's simplify the term (4xy^2)^3. To raise each term inside the parentheses to the power outside the parentheses, we have:
(4xy^2)^3 = (4^3)(x^3)(y^2*3) = 64x^3y^6
Now, let's simplify the term (xy)^5. To raise each term inside the parentheses to the power outside the parentheses, we have:
(xy)^5 = (x^1y^1)^5 = x^(1*5)y^(1*5) = x^5y^5
Finally, let's multiply the two simplified terms together:
64x^3y^6 * x^5y^5 = (64 * x^3 * x^5) * (y^6 * y^5) = 64x^(3+5)y^(6+5) = 64x^8y^11
Therefore, the simplified expression is 64x^8y^11.
The correct answer is A. 64x^8y^11.
11 months ago
To simplify the expression (4xy^2)^3(xy)^5, we need to apply both the power of a product rule and the power of a power rule.
First, let's simplify the expression inside the parentheses (4xy^2)^3:
To raise a product to a power, we need to raise each factor individually to that power.
(4xy^2)^3 = (4^3)(x^3)(y^2)^3
= 64x^3y^6
Next, let's simplify the expression outside the parentheses (xy)^5:
To raise a power to another power, we need to multiply the exponents.
(xy)^5 = x^5y^5
Now, we can combine the two simplified expressions:
(4xy^2)^3(xy)^5 = (64x^3y^6)(x^5y^5)
To simplify further, we multiply the coefficients (numbers), and combine the variables with the same base by adding their exponents:
(64x^3y^6)(x^5y^5) = 64x^8y^11
Therefore, the simplified expression is 64x^8y^11.
So the correct answer is A. 64x^8y^11.