Simplify (4xy^2)^3 (xy)^5.
A. 64x^8 y^11
B. 64x^15 y^30
C. 12x^2 y^11
D. 12x^8 y^11
A
Simplify (2t^-3)^3 (0.4r)^2.
A. 3.2r^2
B. (1.28r^2)/(t^-6)
C. (1.28r^2)/(t^9)
D. (0.8r^2)/(t^-6)
C
Unit 2 lesson 4 Quiz
1. B
2. A
3. C
4. A
5. D
6. A
7. B
8. C
9. A
10. C
yes A
yes c
To simplify the expression (4xy^2)^3 (xy)^5, we need to follow the rules of exponents.
First, let's simplify the expression inside the first set of parentheses, (4xy^2)^3. To raise a power to a power, we multiply the exponents.
(4xy^2)^3 = 4^3 * x^3 * (y^2)^3
= 64x^3 * y^(2*3)
= 64x^3 * y^6
Next, let's simplify the expression inside the second set of parentheses, (xy)^5. To raise a product to a power, we raise each factor to the power.
(xy)^5 = x^5 * y^5
Now, let's simplify the entire expression by combining the simplified expressions from the two sets of parentheses.
(4xy^2)^3 (xy)^5 = (64x^3 * y^6) * (x^5 * y^5)
= 64x^3 * x^5 * y^6 * y^5
= 64x^(3+5) * y^(6+5)
= 64x^8 * y^11
Therefore, the correct answer is A. 64x^8 y^11.
To solve the second problem, (2t^-3)^3 (0.4r)^2, we follow the same rules of exponents.
First, let's simplify the expression inside the first set of parentheses, (2t^-3)^3. To raise a power to a power, we multiply the exponents.
(2t^-3)^3 = 2^3 * (t^-3)^3
= 8 * t^(-3*3)
= 8 * t^-9
Next, let's simplify the expression inside the second set of parentheses, (0.4r)^2. To raise a product to a power, we raise each factor to the power.
(0.4r)^2 = (0.4)^2 * r^2
= 0.16 * r^2
Now, let's simplify the entire expression by combining the simplified expressions from the two sets of parentheses.
(2t^-3)^3 (0.4r)^2 = (8 * t^-9) * (0.16 * r^2)
= 8 * 0.16 * (t^-9 * r^2)
= 1.28 * (t^-9 * r^2)
= 1.28r^2 / t^9
Therefore, the correct answer is C. (1.28r^2)/(t^9).