Question

Express the following expression as a product of prime factors only in exponential form: $729\times 64$

• A. $3^3\times 2^2$
• B. $3^6\times 2^6$
• C. $6^3\times 6^2$
• D. $2^3\times 3^2$

Answer 1

The correct option is B $3^6\times 2^6$

Prime factorisation of $729$:
$$\begin{array}{cc}3& 729\\ 3& 243\\ 3& 81\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$$
$729=3^6$

Prime factorisation of $64$:
$$\begin{array}{cc}2& 64\\ 2& 32\\ 2& 16\\ 2& 8\\ 2& 4\\ 2& 2\\ & 1\end{array}$$
$64=2^6$

$729\times 64=3^6\times 2^6$