Answer:

Step-by-step explanation:
This question is on rules of rational exponential
where the exponential is a fraction, you can re-write it using radicals where the denominator of the fraction becomes the index of the radical;
<u>General expression </u>
![a^\frac{1}{n} =\sqrt[n]{a}](https://tex.z-dn.net/?f=a%5E%5Cfrac%7B1%7D%7Bn%7D%20%3D%5Csqrt%5Bn%5D%7Ba%7D)
Thus ![\sqrt[3]{x} =x^\frac{1}{3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%7D%20%3Dx%5E%5Cfrac%7B1%7D%7B3%7D)
<u>Applying the same in the question </u>
![\sqrt[3]{x^5y} =x^\frac{5}{3} y^\frac{1}{3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E5y%7D%20%3Dx%5E%5Cfrac%7B5%7D%7B3%7D%20y%5E%5Cfrac%7B1%7D%7B3%7D)
=
The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is 
<h3>How to determine the equation of the hyperbola?</h3>
The given parameters are:
- Directrices at x = ±2
- Foci at (5, 0) and (−5, 0)
The foci of a hyperbola are represented as:
Foci = (k ± c, h)
The center is:
Center = (h,k)
And the directrix is:
Directrix, x = h ± a²/c
By comparison, we have:
k ± c = ±5
h = 0
h ± a²/c = ±2
Substitute h = 0 in h ± a²/c = ±2
0 ± a²/c = ±2
This gives
a²/c = 2
Multiply both sides by c
a² = 2c
k ± c = ±5 means that:
k ± c = 0 ± 5
By comparison, we have:
k = 0 and c = 5
Substitute c = 5 in a² = 2c
a² = 2 * 5
a² = 10
Next, we calculate b using:
b² = c² - a²
This gives
b² = 5² - 10
Evaluate
b² = 15
The hyperbola is represented as:

So, we have:

Evaluate

Hence, the equation of the hyperbola is 
Read more about hyperbola at:
brainly.com/question/3405939
#SPJ1
Answer:
the last one
Step-by-step explanation:
In the last one, it takes all of the numbers in the one parentheses and distributes it to the 0.5.
Look at the picture. (sorry for the messy writing)
Answer:
f(9)=54
Step-by-step explanation:
Subsitute 9 for x in f(x)=6x

The answer to this question is 8/10 which also equals 4/5