# Simplify: {(6^6)^4 -: (6^7)^0 xx[(6^2)^3]^2}^2 -: {[(6^3)^5xx(6^2)^3]^3 : [(6^3)^3]^4}^2?

Apr 26, 2016

${6}^{18}$

#### Explanation:

${\left\{{\left({6}^{6}\right)}^{4} \div {\left({6}^{7}\right)}^{0} \times {\left[{\left({6}^{2}\right)}^{3}\right]}^{2}\right\}}^{2} \div {\left\{{\left[{\left({6}^{3}\right)}^{5} \times {\left({6}^{2}\right)}^{3}\right]}^{3} \div {\left[{\left({6}^{3}\right)}^{3}\right]}^{4}\right\}}^{2}$

= ${\left\{{6}^{24} \div {6}^{0} \times {6}^{12}\right\}}^{2} \div {\left\{{\left[{6}^{15} \times {6}^{6}\right]}^{3} \div {\left[{6}^{9}\right]}^{4}\right\}}^{2}$

= ${\left\{{6}^{24 - 0 + 12}\right\}}^{2} \div {\left\{{\left[{6}^{15 + 6}\right]}^{3} \div {6}^{36}\right\}}^{2}$

= ${\left\{{6}^{36}\right\}}^{2} \div {\left\{{\left[{6}^{21}\right]}^{3} \div {6}^{36}\right\}}^{2}$

= ${6}^{72} \div {\left\{{6}^{63} \div {6}^{36}\right\}}^{2}$

= ${6}^{72} \div {\left\{{6}^{63 - 36}\right\}}^{2}$

= ${6}^{72} \div {\left\{{6}^{27}\right\}}^{2}$

= ${6}^{72} \div {6}^{54}$

= ${6}^{72 - 54}$

= ${6}^{18}$