EXERCISE 13.2

$3^0={\left(1000\right)}^0$

If $108\times 192$ can be expressed as $2^a\times 3^b$, find the value of $a$.

If $270$ can be expressed as a product of prime factors only, in exponential form as $2\times b^3\times 5$, find the value of $b$.

If $729\times 64=2^m\times 3^n$, when $729\times 64$ is expressed as product of its prime factors, then find the value of $m$.

If $768=2^m\times n$, when $768$ is expressed as product of its prime factors, then find the value of $m$.

Simplify: $\frac{{\left(2^5\right)}^2\times 7^3}{8^3\times 7}$
 

If simplified form of $\frac{25\times 5^2\times {\mathrm{t}}^8}{{10}^3\times {\mathrm{t}}^4}$ is of the form $\frac{5}{8}{\mathrm{t}}^{\mathrm{n}}$, then find the value of $\mathrm{n}$.
 

Simplify: $\frac{3^5\times {10}^5\times 25}{5^7\times 6^5}$