How do you multiply ${(3 n^{2})}^{3} \cdot 2 n^{2}$ $(3n ^ { 2} ) ^ { 3} \cdot 2n ^ { 2}$ ?

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Answer 1 · 2018-06-16T04:28:09

The answer is $54 n^{8}$ $54n^8$

Firstly expand the brackets: ${(3 n^{2})}^{3}$ $(3n^2)^3$ = $3^{3} \cdot n^{2 \cdot 3}$ $3^3*n^(2*3)$

Then collect the coefficients and variables:

= $3^{3} \cdot n^{2 \cdot 3} \cdot 2 n^{2}$ $3^3*n^(2*3)*2n^2$
= $27 \cdot 2 \cdot n^{2 \cdot 3} \cdot n^{2}$ $27*2*n^(2*3)*n^2$

Lastly, multiply the coefficients and add the powers:

= $54 \cdot n^{6 + 2}$ $54*n^(6+2)$
= $54 n^{8}$ $54 n^8$

How do you multiply (3n2)3⋅2n2(3n ^ { 2} ) ^ { 3} \cdot 2n ^ { 2}?