z = 3m - 2n
Step-by-step explanation:
1000^m ÷ 100^n
Rewrite them in exponent form
That's
10^3m ÷ 10^2n
Since the bases are the same and they are dividing we subtract the exponents
That's
10^3m - 2n
Comparing it with 10^z
10^3m - 2n = 10^z
z = 3m - 2n
Hope this helps you
Answer:
1/2
Step-by-step explanation:
cotangent is the reciprocal of a tangent
tanθ = 2
cotθ = 1/2
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.