Question

Find the value of K in the following equation:
(((-5)/(11)))^(k+2)-: (((-5)/(11)))^(-4k+5)=(((-5)/(11)))^(2)k

Answer 1

Answer:

K=1

Step-by-step explanation:

Is this the way to write? Small brackets enclosing small brackets? And is that the sign for division?

correct expression:

{(-5/11)^(K+2)} ÷ {(-5/11)^(-4K+5)} = {(-5/11)^(2K)}

All bases are same, so equating the powers:

(when equating the powers ÷ means - and × means +)

K+2 - (-4K+5) = 2K

2 + 4K - 5 = K

3K = 3

K = 1

Answer 2

(((-5)/(11)))^(k+2)-: (((-5)/(11)))^(-4k+5)=(((-5)/(11)))^(2)k

Given,

(((-5)/(11)))^(-4k+5)=(((-5)/(11)))^(2)k

$(\dfrac{-5}{11})^{-4k+5} = (\dfrac{-5}{11})^{2k}$

Taking log on both sides, we get,

$(-4k+5) log (\dfrac{-5}{11}) = (2k) log (\dfrac{-5}{11})$

-4k + 5 = 2k

-4k - 2k = -5

-6k = -5

k = 5/6

Now,

(((-5)/(11)))^(k+2)

$(\dfrac{-5}{11})^{k+2}\\\\=(\dfrac{-5}{11})^{\frac{5}{6}+2}\\\\=(\dfrac{-5}{11})^{\frac{17}{6}}$