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How do you multiply and simplify ${(- 3 x^{3} y^{4} z^{3})}^{3} (2 y z^{2})$ $(- 3x ^ { 3} y ^ { 4} z ^ { 3} ) ^ { 3} ( 2y z ^ { 2} )$ ?

1 Answer

Shwetank Mauria

Jun 13, 2017

${(- 3 x^{3} y^{4} z^{3})}^{3} (2 y z^{2}) = - 54 x^{9} y^{13} z^{11}$ $(-3x^3y^4z^3)^3(2yz^2)=-54x^9y^13z^11$

Explanation:

As ${(a^{m})}^{n} = a^{(m \times n)}$ $(a^m)^n=a^((mxxn))$ and $a^{m} \times a^{n} = a^{(m + n)}$ $a^mxxa^n=a^((m+n))$

${(- 3 x^{3} y^{4} z^{3})}^{3} (2 y z^{2})$ $(-3x^3y^4z^3)^3(2yz^2)$

= $({(- 3)}^{3} x^{3 \times 3} y^{4 \times 3} z^{3 \times 3}) (2 y z^{2}$ $((-3)^3x^(3xx3)y^(4xx3)z^(3xx3))(2yz^2$

= $(- 27 x^{9} y^{12} z^{9}) \times (2 y z^{2})$ $(-27x^9y^12z^9)xx(2yz^2)$

= $(- 27) \times 2 \times x^{9} y^{12 + 1} z^{9 + 2}$ $(-27)xx2xxx^9y^(12+1)z^(9+2)$

= $- 54 x^{9} y^{13} z^{11}$ $-54x^9y^13z^11$

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