Find the simplified form of each expression.
1.(4/7y^5)^2
A.8/14y^10
B.16/49y^25
C.16/49y^10
D.8/14y^25
2.(x/2y^5)^-2
A.x^2/4y^10
B.4y^25/x^2
C.4y^10/x^2
D.x^2/4y^25
I think #1 is A and #2 is A
Please correct me if I'm wrong.
anyone got full test answers
Well, let's see if we can find the correct answers together!
1. (4/7y^5)^2 - To simplify this expression, we need to square both the numerator and the denominator separately. So, (4/7)^2 will be (4^2)/(7^2) which equals 16/49. Now let's simplify the denominator: (y^5)^2 is the same as y^(5*2) which is y^10. Therefore, the simplified form of (4/7y^5)^2 is C. 16/49y^10.
2. (x/2y^5)^-2 - To simplify this expression, we need to invert the entire fraction and then square it. Inverting (x/2y^5) gives us (2y^5/x). Now let's square it: (2y^5/x)^2 is equal to (2^2y^10)/(x^2). Simplifying, we get 4y^10/x^2. So, the simplified form of (x/2y^5)^-2 is A. x^2/4y^10.
Great job on #1! But for #2, the correct answer is A instead of B. So, your revised answers are:
1. C. 16/49y^10
2. A. x^2/4y^10
Keep up the good work!
You are correct about question #2. The simplified form of (x/2y^5)^-2 is A, x^2/4y^10.
However, for question #1, the simplified form of (4/7y^5)^2 is C, 16/49y^10.
To simplify the expression, you need to square both the numerator and denominator.
So, (4/7y^5)^2 = (4^2)/(7^2 y^5)^2 = (16/49y^10)
To find the simplified form of each expression, we need to apply the exponent rules.
1. (4/7y^5)^2:
To find the squared form of this expression, we square both the numerator and the denominator separately. In this case, we square 4 and get 16, and we square y^5 and get y^10. The expression becomes (16/49y^10).
Looking at the answer choices:
A. 8/14y^10: This can be simplified further by dividing both the numerator and denominator by 8, resulting in 1/2y^10. So, A is not the correct answer.
B. 16/49y^25: This matches the simplified form of the expression, so B is the correct answer.
C. 16/49y^10: This matches the simplified form of the expression, so C is also a correct answer.
D. 8/14y^25: This can be simplified further by dividing both the numerator and denominator by 2, resulting in 4/7y^25. So, D is not the correct answer.
Therefore, the correct answer for #1 is either B or C.
2. (x/2y^5)^-2:
To find the negative exponent form of this expression, we take the reciprocal of the whole expression and apply the square of the exponent. So, the reciprocal of (x/2y^5) is (2y^5/x), and we square the exponent -2, resulting in 4y^10/x^2. The expression becomes 4y^10/x^2.
Looking at the answer choices:
A. x^2/4y^10: This can be simplified further by taking the reciprocal, resulting in 1/4xy^10. So, A is not the correct answer.
B. 4y^25/x^2: This matches the simplified form of the expression, so B is the correct answer.
C. 4y^10/x^2: This matches the simplified form of the expression, so C is also a correct answer.
D. x^2/4y^25: This can be simplified further by taking the reciprocal, resulting in 1/4xy^25. So, D is not the correct answer.
Therefore, the correct answer for #2 is either B or C.
Your answer for #1 being A is incorrect, but your answer for #2 being A is correct. The correct answers are:
1. (4/7y^5)^2 = 16/49y^10, either B or C.
2. (x/2y^5)^-2 = 4y^10/x^2, either B or C.
Two strikes
(4/7y^5)^2
= (4/7y^5)(4/7y^5)
= (16/49) y^10
(x/2y^5)^-2
= (2y^5/x)^2
= 4 y^10 / x^2