Question

Simplify and write the following in exponential form : $\frac{{\left(6^3\right)}^2\times {\left(-3^2\right)}^2}{18\times {\left(3\right)}^3}$

Answer 1

Given that , $\frac{{\left(6^3\right)}^2\times {\left(-3^2\right)}^2}{18\times {\left(3\right)}^3}$

$=\frac{6^{2\times 3}\times {\left(-3\right)}^{2\times 2}}{18\times {\left(3\right)}^3}$

$=\frac{6^6\times {\left(-3\right)}^4}{18\times {\left(3\right)}^3}$

$=\frac{6^6\times {\left(-1\right)}^4\times {\left(3\right)}^4\times {\left(3\right)}^{-3}}{18}$

$=\frac{6\times 6^5\times 1\times {\left(3\right)}^{4-3}}{18}$

$=\frac{6^5\times 3}{3}$

$=6^5$

Hence , the required value is $6^{5}or7776$.