The expression with a rational exponent of the seventh root of x to the third power is x to the three sevenths power ⇒ answer A
Step-by-step explanation:
Let us explain how to change the radical expression as an expression
with a rational exponent
1. Find the number of the root and make it the denominator of the
fraction exponent
2. Find the power of the term under the radical and make it the
numerator of the fraction exponent
Examples:
![\sqrt[3]{x^{n}}=x^{\frac{n}{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E%7Bn%7D%7D%3Dx%5E%7B%5Cfrac%7Bn%7D%7B3%7D%7D)
![\sqrt[5]{x^{n}}=x^{\frac{n}{5}}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7Bx%5E%7Bn%7D%7D%3Dx%5E%7B%5Cfrac%7Bn%7D%7B5%7D%7D)
So ![\sqrt[m]{x^{n}}=x^{\frac{n}{m}}](https://tex.z-dn.net/?f=%5Csqrt%5Bm%5D%7Bx%5E%7Bn%7D%7D%3Dx%5E%7B%5Cfrac%7Bn%7D%7Bm%7D%7D)
∵ the radical expression is the seventh root of x to the third power
∵ seventh root = ![\sqrt[7]{}](https://tex.z-dn.net/?f=%5Csqrt%5B7%5D%7B%7D)
∵ x to the third power = x³
∴ seventh root of x to the third power = ![\sqrt[7]{x^{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B7%5D%7Bx%5E%7B3%7D%7D)
Let us change it to the rational exponent
∵
∵
∴ m = 7 and n = 3
∴ = 
∵ is x to the three sevenths power
∴ is x to the three sevenths power
The expression with a rational exponent of the seventh root of x to the third power is x to the three sevenths power
Learn more:
You can learn more about radical equation is brainly.com/question/7153188
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You need to understand that you're solving for the average, which you already know: 90. Since you know the values of the first three exams, and you know what your final value needs to be, just set up the problem like you would any time you're averaging something.
Solving for the average is simple:
Add up all of the exam scores and divide that number by the number of exams you took.
(87 + 88 + 92) / 3 = your average if you didn't count that fourth exam.
Since you know you have that fourth exam, just substitute it into the total value as an unknown, X:
(87 + 88 + 92 + X) / 4 = 90
Now you need to solve for X, the unknown:
87
+
88
+
92
+
X
4
(4) = 90 (4)
Multiplying for four on each side cancels out the fraction.
So now you have:
87 + 88 + 92 + X = 360
This can be simplified as:
267 + X = 360
Negating the 267 on each side will isolate the X value, and give you your final answer:
X = 93
Now that you have an answer, ask yourself, "does it make sense?"
I say that it does, because there were two tests that were below average, and one that was just slightly above average. So, it makes sense that you'd want to have a higher-ish test score on the fourth exam.
Answer: Use the distributive property to multiply 3 by y−4.
3y−12−2(y−4)
Use the distributive property to multiply −2 by y−4.
3y−12−2y+8
Combine 3y and −2y to get y.
y−12+8
Add −12 and 8 to get −4.
Anwser:
y−4
Step-by-step explanation:
Hope this helps!
