We are asked to multiply two numbers written in scientific notation: $(5.84 \times 10^{-9})$ and $(2.5 \times 10^{10})$.

1. Problem Description

We are asked to multiply two numbers written in scientific notation: $(5.84 \times 10^{-9})$ and $(2.5 \times 10^{10})$.

2. Solution Steps

First, we multiply the coefficients:

$5.84 \times 2.5 = 14.6$

Next, we multiply the powers of 10:

$10^{-9} \times 10^{10} = 10^{-9 + 10} = 10^{1}$

So, the product is:

$14.6 \times 10^{1}$

$14.6 \times 10^1 = 1.46 \times 10 \times 10^1 = 1.46 \times 10^2$

3. Final Answer

$1.46 \times 10^{2}$