Question

express each of the following as aproduct of prime factors only in exponential form 192×729​

Answer 1

Step-by-step explanation:

$\\ \begin{aligned} \begin{array}{c|c} 2 & 192 \\ \hline 2 & 96 \\ \hline 2 & 48 \\ \hline 2 & 24 \\ \hline 2 & 12 \\ \hline 2 & 6 \\ \hline 3 & 3 \\ \hline & 1 \end{array} \\ \\ \therefore 192 &=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \\ &=2^{6} \times 3 \end{aligned}$

$\begin{array}{l}\begin{array}{c|c} 3 & 729 \\ \hline 3 & 243 \\ \hline 3 & 81 \\ \hline 3 & 27 \\ \hline 3 & 9 \\ \hline 3 & 3 \\ \hline & 1 \end{array} \\ \\ \therefore \: 729 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \\ \\ \: \quad \qquad = {3}^{6} \end{array}$

$\begin{array}{l}192 \times 729 = {2}^{6} \times 3 \times {3}^{6} \\ \boxed{\red{ 192 \times 729 = {2}^{6} \times {3}^{7} }} \end{array}$

Answer 2

Step-by-step explanation:

$\\ \begin{aligned} \begin{array}{c|c} 2 & 192 \\ \hline 2 & 96 \\ \hline 2 & 48 \\ \hline 2 & 24 \\ \hline 2 & 12 \\ \hline 2 & 6 \\ \hline 3 & 3 \\ \hline & 1 \end{array} \\ \\ \therefore 192 &=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \\ &=2^{6} \times 3 \end{aligned}$

$\begin{array}{l}\begin{array}{c|c} 3 & 729 \\ \hline 3 & 243 \\ \hline 3 & 81 \\ \hline 3 & 27 \\ \hline 3 & 9 \\ \hline 3 & 3 \\ \hline & 1 \end{array} \\ \\ \therefore \: 729 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \\ \\ \: \quad \qquad = {3}^{6} \end{array}$

$\begin{array}{l}192 \times 729 = {2}^{6} \times 3 \times {3}^{6} \\ \boxed{\red{ 192 \times 729 = {2}^{6} \times {3}^{6} }} \end{array}$