Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
12
x
9
y
4
6
x
3
y
2
A.
2
x
3
y
2
B.
2
x
6
y
2
C.
2
x
3
y
2
D.
2
x
6
y
2
Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
12
x
9
y
4
6
x
3
y
2
A.
2
x
3
y
2
B.
2
x
6
y
2
C.
2
x
3
y
2
D.
2
x
6
y
2
C.
To simplify the expression, we can first simplify the numerator and denominator separately:
Numerator:
12 ÷ 4 = 3
6 ÷ 3 = 2
Denominator:
9 ÷ 3 = 3
2 ÷ 1 = 2
Plugging these simplified values back into the original expression gives:
(3/x) / (3/2y) = (3/1 * 2y/3) / (x/1 * 2/1) = 6y/3x = 2y/x
Therefore, the equivalent expression is 2y/x, which matches option C.
To find the expression that is equivalent to the given expression, we can simplify it by combining the terms in the numerator and the denominator.
Given expression:
12 / (9 * x^4 * y^6)
To simplify:
12 can be written as 2 * 2 * 3
9 can be written as 3 * 3
x^4 can be written as x * x * x * x
y^6 can be written as y * y * y * y * y * y
So the expression becomes:
(2 * 2 * 3) / ((3 * 3) * (x * x * x * x) * (y * y * y * y * y * y))
Now, we can cancel out common factors:
2/3 from the numerator and 3/3 from the denominator can be canceled out:
(2 * 2) / ((x * x * x * x) * (y * y * y * y * y * y))
Simplifying further:
4 / (x^4 * y^6)
Therefore, the expression that is equivalent to the given expression is:
4 / (x^4 * y^6)
The correct answer is D. 2x^6 * y^2
To find an equivalent expression, we need to simplify the given expression:
12/(9xy^4) * (6x^3y^2)
To multiply fractions, multiply the numerators together and the denominators together:
(12 * 6 * x * x^3 * y * y^2) / (9xy^4)
Simplifying the numerator:
= 72x^4y^3
Simplifying the denominator:
= 9xy^4
Combining the numerator and the denominator:
= (72x^4y^3) / (9xy^4)
Canceling out common factors:
= (8x^3) / y
Therefore, the expression is equivalent to 2x^3 / y, which is equivalent to option C.