9514 1404 393
Answer:
a.
Step-by-step explanation:
For an even-index radical, ...
![\sqrt[n]{x^n}=|x|\qquad\text{n even}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%5En%7D%3D%7Cx%7C%5Cqquad%5Ctext%7Bn%20even%7D)
This lets us simplify the given expression as follows:
![\sqrt[4]{81x^6y^4}-|y|\sqrt[4]{x^6}-\sqrt[4]{16x^2}=\sqrt[4]{(3xy)^4x^2}-|y|\sqrt[4]{x^4x^2}-\sqrt[4]{2^4x^2}\\\\=3|xy|\sqrt[4]{x^2}-|xy|\sqrt[4]{x^2}-2\sqrt[4]{x^2}=\boxed{2|xy|\sqrt[4]{x^2}-2\sqrt[4]{x^2}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B81x%5E6y%5E4%7D-%7Cy%7C%5Csqrt%5B4%5D%7Bx%5E6%7D-%5Csqrt%5B4%5D%7B16x%5E2%7D%3D%5Csqrt%5B4%5D%7B%283xy%29%5E4x%5E2%7D-%7Cy%7C%5Csqrt%5B4%5D%7Bx%5E4x%5E2%7D-%5Csqrt%5B4%5D%7B2%5E4x%5E2%7D%5C%5C%5C%5C%3D3%7Cxy%7C%5Csqrt%5B4%5D%7Bx%5E2%7D-%7Cxy%7C%5Csqrt%5B4%5D%7Bx%5E2%7D-2%5Csqrt%5B4%5D%7Bx%5E2%7D%3D%5Cboxed%7B2%7Cxy%7C%5Csqrt%5B4%5D%7Bx%5E2%7D-2%5Csqrt%5B4%5D%7Bx%5E2%7D%7D)
We have sequence equation 
.
In this case n is a natural number (1, 2, 3, ...).
So start inserting and computing value of 
given that you know the value of n and a.
(first term)
Hope this helps.
Answer:
The smallest solution is -6
Step-by-step explanation:
2/3 x^2=24
Multiply by 3/2 on each side
3/2 *2/3 x^2=24 *3/2
x^2 = 36
Take the square root of each side
sqrt(x^2) = ±sqrt(36)
x = ±6
x = -6, 6
The smallest solution is -6
Answer:
X= 9/2
Alternative form
x=4 1/2, x=4.5
Step-by-step explanation:
*= Multiply
1. log (little 10 under) (2)*(3x-1)= log (little 10 under) (2)*(x+8)
2. then divide both side by log (little 10 under (2))
3. 3x-1=x+8
4. move variable to the left side and change its sign
5. 3x-x-1=8
6. then move constant to the right side and change its sign
7. 3x-x=8+1
8. collect like terms
9. 2x=8+1
10. add 8+1
11. 2x=9
12. then divide both sides by 2
13. 2/2 9/2
14. 2/2 cancels out so x=9/2 is the answer
Answer:
x = -6
Step-by-step explanation:
(2x/3) + 10 = (x/5) + (36/5)
15*[(2x/3) + 10 = (x/5) + (36/5)] <em>[Multiply both sides by 15 in order to convert the fractions to whole numbers]</em>
(15/3)*2x +15*10 = (15/5)x + (15/5)*36
5*2x + 150 = 3x + 3*36
10x +150 = 3x + 108
7x = -42
x = -6
===
<u>Check:</u>
Does (2x/3) + 10 = (x/5) + (36/5) work for x = -6?
(2(-6)/3) + 10 = (-6/5) + (36/5) ?
-4 + 10 = (30/5) ?
6 = 6 YES
