Answer:
A. ![(\sqrt[3]{125})^9\ and\ (125)^{\frac{9}{3}}](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7B125%7D%29%5E9%5C%20and%5C%20%28125%29%5E%7B%5Cfrac%7B9%7D%7B3%7D%7D)
D. 
Step-by-step explanation:
Equivalent expressions are those expressions that simplify to same form.
Now, let us check each of the given options.
Option A:
We know that,
![\sqrt[n]{x} =x^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%20%3Dx%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
Therefore, ![\sqrt[3]{125} =(125)^{\frac{1}{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B125%7D%20%3D%28125%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
Thus the first expression becomes;
Now, using law of indices 
, we get
Therefore, are equivalent.
Option B:
Consider the second expression 
We know that,
Therefore, 
. Hence, the expressions are not equivalent.
Option C:
We know that,
![x^{\frac{1}{n}}=\sqrt[n]{x}](https://tex.z-dn.net/?f=x%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D%3D%5Csqrt%5Bn%5D%7Bx%7D)
Therefore, ![4^{\frac{1}{5}}=\sqrt[5]{4}](https://tex.z-dn.net/?f=4%5E%7B%5Cfrac%7B1%7D%7B5%7D%7D%3D%5Csqrt%5B5%5D%7B4%7D)
Now, ![\sqrt[5]{4}\ne (\sqrt 4)^5](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B4%7D%5Cne%20%28%5Csqrt%204%29%5E5)
Therefore, the expressions are not equivalent.
Option D:
Using law of indices 
, we get
Now, we know that, 
So, 
Therefore, are equivalent.
Answer:
13
Step-by-step explanation:
1) 4
2) 5
3) 6
4 )7
5) 8
6) 9
7) 10
8) 11
9) 12
10) 13
Answer:
78
Step-by-step explanation:
x + 21 = 3x - 15
- x - x
21 = 2x - 15
+ 15 + 15
36 = 2x
/ 2 / 2
18 = x
2 (x + 21)
2 (18 + 21)
36 + 42
78
Answer:
x = -4, y = 9
or
(-4, 9)
Step-by-step explanation:
x - 5y = -49
y = -2x + 1
substitute y for -2x + 1
x - 5(-2x + 1) = -49
x + 10x - 5 = - 49
add 5 to both sides
x + 10x - 5 + 5 = - 49 + 5
x + 10x = -44
11x = -44
divide both sides by 11
11x/11 = -44/11
x = -4
substitute x for -4 in any of the original equations
y = -2x + 1
y = -2 * -4 + 1
y = 8 + 1
y = 9
Step-by-step explanation:
90×3×-5×-2/3×-5
2700/-15
-180
