For this case we must multiply the following expression:
![\sqrt [3] {x ^ 2} * \sqrt [4] {x ^ 3}](https://tex.z-dn.net/?f=%5Csqrt%20%5B3%5D%20%7Bx%20%5E%202%7D%20%2A%20%5Csqrt%20%5B4%5D%20%7Bx%20%5E%203%7D)
By definition of properties of otencias and roots we have:
![\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}](https://tex.z-dn.net/?f=%5Csqrt%20%5Bn%5D%20%7Ba%20%5E%20m%7D%20%3D%20a%20%5E%20%7B%5Cfrac%20%7Bm%7D%20%7Bn%7D%7D)
We rewrite the terms of the expression:
![\sqrt [3] {x ^ 2} = (x ^ 2) ^ {\frac {1} {3}} = (x ^ 2) ^ {\frac {4} {12}}\\\sqrt [4] {x ^ 3} = (x ^ 3) ^ {\frac {1} {4}} = (x ^ 3) ^ {\frac {3} {12}}](https://tex.z-dn.net/?f=%5Csqrt%20%5B3%5D%20%7Bx%20%5E%202%7D%20%3D%20%28x%20%5E%202%29%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B3%7D%7D%20%3D%20%28x%20%5E%202%29%20%5E%20%7B%5Cfrac%20%7B4%7D%20%7B12%7D%7D%5C%5C%5Csqrt%20%5B4%5D%20%7Bx%20%5E%203%7D%20%3D%20%28x%20%5E%203%29%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B4%7D%7D%20%3D%20%28x%20%5E%203%29%20%5E%20%7B%5Cfrac%20%7B3%7D%20%7B12%7D%7D)
So, we have:
![(x ^ 2) ^ {\frac {4} {12}} * (x ^ 3) ^ {\frac {3} {12}} =](https://tex.z-dn.net/?f=%28x%20%5E%202%29%20%5E%20%7B%5Cfrac%20%7B4%7D%20%7B12%7D%7D%20%2A%20%28x%20%5E%203%29%20%5E%20%7B%5Cfrac%20%7B3%7D%20%7B12%7D%7D%20%3D)
Applying the above definition we have:
![\sqrt [12] {(x ^ 2) ^ 4} * \sqrt [12] {(x ^ 3) ^ 3} =](https://tex.z-dn.net/?f=%5Csqrt%20%5B12%5D%20%7B%28x%20%5E%202%29%20%5E%204%7D%20%2A%20%5Csqrt%20%5B12%5D%20%7B%28x%20%5E%203%29%20%5E%203%7D%20%3D)
We multiply the exponents:
![\sqrt [12] {x ^ 8} * \sqrt [12] {x ^ 9} =](https://tex.z-dn.net/?f=%5Csqrt%20%5B12%5D%20%7Bx%20%5E%208%7D%20%2A%20%5Csqrt%20%5B12%5D%20%7Bx%20%5E%209%7D%20%3D)
We combine using the product rule for radicals.
![\sqrt [12] {x ^ 8 * x ^ 9} =](https://tex.z-dn.net/?f=%5Csqrt%20%5B12%5D%20%7Bx%20%5E%208%20%2A%20x%20%5E%209%7D%20%3D)
By definition of multiplication properties of powers of the same base, we put the same base and add the exponents:
![\sqrt [12] {x ^ {8 + 9}} =\\\sqrt [12] {x ^ {17}} =\\\sqrt [12] {x ^ {12} * x ^ 5} =\\x \sqrt [12] {x ^ 5}](https://tex.z-dn.net/?f=%5Csqrt%20%5B12%5D%20%7Bx%20%5E%20%7B8%20%2B%209%7D%7D%20%3D%5C%5C%5Csqrt%20%5B12%5D%20%7Bx%20%5E%20%7B17%7D%7D%20%3D%5C%5C%5Csqrt%20%5B12%5D%20%7Bx%20%5E%20%7B12%7D%20%2A%20x%20%5E%205%7D%20%3D%5C%5Cx%20%5Csqrt%20%5B12%5D%20%7Bx%20%5E%205%7D)
Answer:
Option C
Answer:
The correct answer is (40, 60) and (80,120) D
Step-by-step explanation:
Answer:
x>-4
Step-by-step explanation:
Divide by negative 4 on both sides, and since its a negative, you have to flip the inequality sign, so it comes out to be x> -4
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Hope this helps! :)
You answer will be 8:1 is 16 ounces hope that helps you.