A wire has a resistance of 45 Ω. It is cut into 5 equal pieces, and the pieces are joined side by…

Step 1. One piece. Each piece has a fifth of the length, so $R_1 = \dfrac{45\ \Omega}{5} = 9\ \Omega$.

Step 2. Five side by side. The same area is repeated five times, so the area becomes $5$ times larger. The bundle has $\dfrac{9\ \Omega}{5} = 1.8\ \Omega$. In general, $R_{\text{bundle}} = \dfrac{R}{n^2}$.

Step 3. The number of pieces. We want $\dfrac{45\ \Omega}{n^2} = 0.45\ \Omega$, so $n^2 = 100$ and $n = 10$.