Solve {(729^{4}b^{5})^{2}(144a^{9}b^3c^4)^3}^4}

$$\{ ( 729 ^ { 4 } b ^ { 5 } ) ^ { 2 } ( 144 a ^ { 9 } b ^ { 3 } c ^ { 4 } ) ^ { 3 } \} ^ { 4 } \}$$

Evaluate

$$3218331761735798192409710281533272230493273493710800555851328951269491058406422969418458651005659604178651141925502976c^{48}b^{76}a^{108}$$

Solution Steps

Calculate 729 to the power of 4 and get 282429536481.

$$\left(\left(282429536481b^{5}\right)^{2}\times \left(144a^{9}b^{3}c^{4}\right)^{3}\right)^{4}$$

Expand \left(282429536481b^{5}\right)^{2}.

$$\left(282429536481^{2}\left(b^{5}\right)^{2}\times \left(144a^{9}b^{3}c^{4}\right)^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\left(282429536481^{2}b^{10}\times \left(144a^{9}b^{3}c^{4}\right)^{3}\right)^{4}$$

Calculate 282429536481 to the power of 2 and get 79766443076872509863361.

$$\left(79766443076872509863361b^{10}\times \left(144a^{9}b^{3}c^{4}\right)^{3}\right)^{4}$$

Expand \left(144a^{9}b^{3}c^{4}\right)^{3}.

$$\left(79766443076872509863361b^{10}\times 144^{3}\left(a^{9}\right)^{3}\left(b^{3}\right)^{3}\left(c^{4}\right)^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.

$$\left(79766443076872509863361b^{10}\times 144^{3}a^{27}\left(b^{3}\right)^{3}\left(c^{4}\right)^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(79766443076872509863361b^{10}\times 144^{3}a^{27}b^{9}\left(c^{4}\right)^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\left(79766443076872509863361b^{10}\times 144^{3}a^{27}b^{9}c^{12}\right)^{4}$$

Calculate 144 to the power of 3 and get 2985984.

$$\left(79766443076872509863361b^{10}\times 2985984a^{27}b^{9}c^{12}\right)^{4}$$

Multiply 79766443076872509863361 and 2985984 to get 238181322764452084491838132224.

$$\left(238181322764452084491838132224b^{10}a^{27}b^{9}c^{12}\right)^{4}$$

To multiply powers of the same base, add their exponents. Add 10 and 9 to get 19.

$$\left(238181322764452084491838132224b^{19}a^{27}c^{12}\right)^{4}$$

Expand \left(238181322764452084491838132224b^{19}a^{27}c^{12}\right)^{4}.

$$238181322764452084491838132224^{4}\left(b^{19}\right)^{4}\left(a^{27}\right)^{4}\left(c^{12}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 19 and 4 to get 76.

$$238181322764452084491838132224^{4}b^{76}\left(a^{27}\right)^{4}\left(c^{12}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 27 and 4 to get 108.

$$238181322764452084491838132224^{4}b^{76}a^{108}\left(c^{12}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 12 and 4 to get 48.

$$238181322764452084491838132224^{4}b^{76}a^{108}c^{48}$$

Calculate 238181322764452084491838132224 to the power of 4 and get 3218331761735798192409710281533272230493273493710800555851328951269491058406422969418458651005659604178651141925502976.

$$3218331761735798192409710281533272230493273493710800555851328951269491058406422969418458651005659604178651141925502976b^{76}a^{108}c^{48}$$

Expand

$$3218331761735798192409710281533272230493273493710800555851328951269491058406422969418458651005659604178651141925502976c^{48}b^{76}a^{108}$$

Solution Steps

Calculate 729 to the power of 4 and get 282429536481.

$$\left(\left(282429536481b^{5}\right)^{2}\times \left(144a^{9}b^{3}c^{4}\right)^{3}\right)^{4}$$

Expand \left(282429536481b^{5}\right)^{2}.

$$\left(282429536481^{2}\left(b^{5}\right)^{2}\times \left(144a^{9}b^{3}c^{4}\right)^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\left(282429536481^{2}b^{10}\times \left(144a^{9}b^{3}c^{4}\right)^{3}\right)^{4}$$

Calculate 282429536481 to the power of 2 and get 79766443076872509863361.

$$\left(79766443076872509863361b^{10}\times \left(144a^{9}b^{3}c^{4}\right)^{3}\right)^{4}$$

Expand \left(144a^{9}b^{3}c^{4}\right)^{3}.

$$\left(79766443076872509863361b^{10}\times 144^{3}\left(a^{9}\right)^{3}\left(b^{3}\right)^{3}\left(c^{4}\right)^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.

$$\left(79766443076872509863361b^{10}\times 144^{3}a^{27}\left(b^{3}\right)^{3}\left(c^{4}\right)^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(79766443076872509863361b^{10}\times 144^{3}a^{27}b^{9}\left(c^{4}\right)^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\left(79766443076872509863361b^{10}\times 144^{3}a^{27}b^{9}c^{12}\right)^{4}$$

Calculate 144 to the power of 3 and get 2985984.

$$\left(79766443076872509863361b^{10}\times 2985984a^{27}b^{9}c^{12}\right)^{4}$$

Multiply 79766443076872509863361 and 2985984 to get 238181322764452084491838132224.

$$\left(238181322764452084491838132224b^{10}a^{27}b^{9}c^{12}\right)^{4}$$

To multiply powers of the same base, add their exponents. Add 10 and 9 to get 19.

$$\left(238181322764452084491838132224b^{19}a^{27}c^{12}\right)^{4}$$

Expand \left(238181322764452084491838132224b^{19}a^{27}c^{12}\right)^{4}.

$$238181322764452084491838132224^{4}\left(b^{19}\right)^{4}\left(a^{27}\right)^{4}\left(c^{12}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 19 and 4 to get 76.

$$238181322764452084491838132224^{4}b^{76}\left(a^{27}\right)^{4}\left(c^{12}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 27 and 4 to get 108.

$$238181322764452084491838132224^{4}b^{76}a^{108}\left(c^{12}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 12 and 4 to get 48.

$$238181322764452084491838132224^{4}b^{76}a^{108}c^{48}$$

Calculate 238181322764452084491838132224 to the power of 4 and get 3218331761735798192409710281533272230493273493710800555851328951269491058406422969418458651005659604178651141925502976.

$$3218331761735798192409710281533272230493273493710800555851328951269491058406422969418458651005659604178651141925502976b^{76}a^{108}c^{48}$$