Answer:
![1. \quad\dfrac{1}{k^{\frac{2}{3}}}\\\\2. \quad\sqrt[7]{x^5}\\\\3. \quad\dfrac{1}{\sqrt[5]{y^2}}](https://tex.z-dn.net/?f=1.%20%5Cquad%5Cdfrac%7B1%7D%7Bk%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%5C%5C%5C%5C2.%20%5Cquad%5Csqrt%5B7%5D%7Bx%5E5%7D%5C%5C%5C%5C3.%20%5Cquad%5Cdfrac%7B1%7D%7B%5Csqrt%5B5%5D%7By%5E2%7D%7D)
Step-by-step explanation:
The applicable rule is ...
![x^{\frac{m}{n}}=\sqrt[n]{x^m}](https://tex.z-dn.net/?f=x%5E%7B%5Cfrac%7Bm%7D%7Bn%7D%7D%3D%5Csqrt%5Bn%5D%7Bx%5Em%7D)
It works both ways, going from radicals to frational exponents and vice versa.
The particular power or root involved can be in either the numerator or the denominator. The transformation applies to the portion of the expression that is the power or root.
First, construct two equations.
Then, equal the two equations to each other like this -
x will be the years.
Type A. Type B
3x + 15 = 4x + 10
- 15. - 15
3x = 4x - 5
-4x. -4x
-x = -5
-x/-1 = -5/-1
x = 5
Check:
3(5) + 15 = 4(5) + 10
15 + 15 = 20 + 10
30 = 30
Therefore, the trees will be the same height in 5 years.
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