1. Indices

You are given that n= 2^2 * 5

Write 40n as the product of its prime factors.

2. $\displaystyle 40=2^3\cdot 5$.
Then $\displaystyle 40n=2^3\cdot 5\cdot 2^2\cdot5=2^5\cdot 5^2$

You are given that n= 2^2 * 5

Write 40n as the product of its prime factors.
$\displaystyle n = 2^2 \cdot 5$

$\displaystyle \Rightarrow 40n = 40 \cdot 2^2 \cdot 5$

$\displaystyle = 8 \cdot 5 \cdot 2^2 \cdot 5$

$\displaystyle = 2^3 \cdot 5 \cdot 2^2 \cdot 5$

$\displaystyle = 2^5 \cdot 5^2$

EDIT: Why am i always the second one to post today?