What is (2a^2b^3c^4)^3(-3ab)^2(-b^3c)^3 ?

The solution to (2a^2b^3c^4)^3(-3ab)^2(-b^3c)^3 is -72a^8b^{20}c^{15}

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simplify (2a^2b^3c^4)^3(-3ab)^2(-b^3c)^3

simplify

(2 a^{2} b^{3} c^{4})^{3} (- 3 ab)^{2} (- b^{3} c)^{3}

- 72 a^{8} b^{20} c^{15}

Solution steps

(2 a^{2} b^{3} c^{4})^{3} (- 3 ab)^{2} (- b^{3} c)^{3}

Simplify

(2 a^{2} b^{3} c^{4})^{3} : 8 a^{6} b^{9} c^{12}

= 8 a^{6} b^{9} c^{12} (- 3 ab)^{2} (- b^{3} c)^{3}

Simplify

(- 3 ab)^{2} : 9 a^{2} b^{2}

= 8 a^{6} b^{9} c^{12} \cdot 9 a^{2} b^{2} (- b^{3} c)^{3}

Simplify

(- b^{3} c)^{3} : - b^{9} c^{3}

= 8 a^{6} b^{9} c^{12} \cdot 9 a^{2} b^{2} (- b^{9} c^{3})

Apply rule:

a (- b) = - ab

8 a^{6} b^{9} c^{12} \cdot 9 a^{2} b^{2} (- b^{9} c^{3}) = - 8 a^{6} b^{9} c^{12} \cdot 9 a^{2} b^{2} b^{9} c^{3}

= - 8 a^{6} b^{9} c^{12} \cdot 9 a^{2} b^{2} b^{9} c^{3}

Multiply the numbers:

- 8 \cdot 9 = - 72

= - 72 a^{6} b^{9} c^{12} a^{2} b^{2} b^{9} c^{3}

Simplify

a^{6} a^{2} : a^{8}

= - 72 a^{8} b^{9} c^{12} b^{2} b^{9} c^{3}

Simplify

b^{9} b^{2} b^{9} : b^{20}

= - 72 a^{8} b^{20} c^{12} c^{3}

Simplify

c^{12} c^{3} : c^{15}

= - 72 a^{8} b^{20} c^{15}

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What is (2a^2b^3c^4)^3(-3ab)^2(-b^3c)^3 ?
The solution to (2a^2b^3c^4)^3(-3ab)^2(-b^3c)^3 is -72a^8b^{20}c^{15}