Why is $\frac{1}{2^\left(l+k\right)} = \left(\frac{1}{2}\right)^\left(l-k\right) * \left(\frac{1}{4}\right)^k$?

Question

I am quite confused about this weird transformation

Answer 1

$$\dfrac{1}{2^{\ell + k}} = \dfrac{1}{2^{\ell - k + 2k}} = \dfrac{1}{2^{\ell - k}\cdot 2^{2k}} = \dfrac{1}{2^{\ell - k}}\cdot \dfrac{1}{2^{2k}} = \left(\dfrac{1}{2}\right)^{\ell - k} \cdot \left(\dfrac{1}{2^2}\right)^k = \left(\dfrac{1}{2}\right)^{\ell - k}\cdot \left(\dfrac{1}{4}\right)^k$$