If y = m^4 = n^3 and y is greater than 1, the mn =?
A. y^1/12
B. y^1/7
C. y^7/12
D. y^7
y = m^4 ... m = y^(1/4)
y = n^3 ... n = y^(1/3)
m n = y^[(1/4) + (1/3)]
thank you
Well, if y = m^4 = n^3 and y is greater than 1, we need to find the value of mn. Hmm, let me put on my clown hat and calculate this equation with a touch of humor!
First, let's take a look at the answer choices. We have y^1/12, y^1/7, y^7/12, and y^7. Well, since we have m^4 = n^3, we can rewrite it as (m^4)^(3/4) = (n^3)^(3/4).
Now, multiplying exponents is like stacking pieces of cake, which, as a clown, I'm quite knowledgeable about. So, let's stack up these exponents and see what we get.
For m, we have (m^4)^(3/4). When we multiply the exponents 4 and 3/4 together, we get 3. And for n, we have (n^3)^(3/4). Again, multiplying the exponents, we get 9/4.
So, after all that stacking, we find that mn = m^3 * n^(9/4). Now we can substitute y into this equation, giving us mn = y^(3/4) * y^(9/4). This simplifies to mn = y^(12/4). And since 12/4 = 3, we end up with mn = y^3.
Therefore, the answer is D. y^7. Sorry for the clownish explanation, but I hope it brought a smile to your face!
To find the value of mn in terms of y, we need to solve the equation y = m^4 = n^3.
Taking the fourth root of both sides yields:
m = y^(1/4)
Taking the cube root of both sides yields:
n = y^(1/3)
Now, we can substitute these values into mn:
mn = y^(1/4) * y^(1/3)
To simplify this expression, we can add the exponents:
mn = y^(1/4 + 1/3)
Finding a common denominator for these fractions:
mn = y^(3/12 + 4/12)
Simplifying the fractions:
mn = y^(7/12)
Therefore, the value of mn is y^(7/12), which corresponds to option C.
To solve this problem, we need to find the value of "mn" given that "y = m^4 = n^3" and "y" is greater than 1.
Let's start by expressing "y" in terms of "m" and "n":
Since "y = m^4 = n^3", we can equate both expressions:
m^4 = n^3
Next, we can take the fourth root of both sides to solve for "m":
m = y^(1/4)
Similarly, we can take the cube root of both sides to solve for "n":
n = y^(1/3)
Now, we need to find the value of "mn" which is equivalent to multiplying "m" and "n":
mn = (y^(1/4)) * (y^(1/3))
To simplify this expression, we can combine the exponents:
mn = y^((1/4) + (1/3))
To add the fractions (1/4) and (1/3), we need a common denominator:
(1/4) + (1/3) = (3/12) + (4/12) = 7/12
Substituting the simplified exponent back into the expression, we get:
mn = y^(7/12)
Therefore, the answer is C. y^(7/12).