Simplify $\ \frac{(0.81)^2 × (0.6×0.21)^2}{35^5 × 0.252} $ into $2^n × 3^m×5^p×7^k$

Question

$\ \frac{(0.81)^2 × (0.6×0.21)^2}{35^5 × 0.252} $

Simplify the following equation into this form :
$2^n × 3^m×5^p×7^k$ where $n, m, p, k$ are integers.

Answer 1

$$\frac{(0.81)^2 × (0.6×0.21)^2}{35^5 × 0.252}$$

$$\frac{\left(\frac{81}{100}\right)^2\times \left(\frac{3}{5}\times \frac{21}{100}\right)^2}{(5\times 7)^5\times \frac{63}{250}}$$

$$\frac{(3^4\times 2^{-2}\times 5^{-2})^2\times (3^2\times 7\times 2^{-2}\times 5^{-3})^2}{5^5\times 7^5 \times 7\times 3^2\times 2^{-1}\times 5^{-3}}$$

$$\frac{3^8\times 2^{-4}\times 5^{-4}\times 3^4\times 7^2\times 2^{-4}\times 5^{-6}}{2^{-1}\times 3^2\times5^2\times 7^6}$$

$$\frac{ 2^{-8}\times 3^{12}\times 5^{-10}\times 7^2}{2^{-1}\times 3^2\times5^2\times 7^6}=2^{-8}\times 3^{12}\times 5^{-10}\times 7^2\times 2^{1}\times 3^{-2}\times 5^{-2}\times 7^{-6}= \color{red}{2^{-7}\times 3^{10}\times 5^{-12}\times 7^{-4}}$$