Question

[(3^6)^3] : ( 3:3^10)^6)

Answer 1

$\left[\left(3^6\right)^3\right]:\left[\left(3:3^{10}\right)^6\right] =\\ \\ = 3^{3\cdot 6}: \left(3^{1-10}\right)^6\\ \\ =3^{18}:\left(3^{-9}\right)^{6}\\ \\ =3^{18}:3^{6\cdot (-9)}\\ \\ =3^{18}:3^{-54}\\ \\ =3^{18-(-54)}\\ \\ = 3^{18+54}\\ \\ = 3^{72}$

Answer 2

[ ( 3⁶ )³ ] : [ ( 3 : 3¹⁰ )⁶ ] =

[ 3^( 6 × 3 ) ] : [ ( 3¹ : 3¹⁰ )⁶ ] =

3¹⁸ : [ ( 3^( 1 - 9 )⁶ ] =

3¹⁸ : [ ( 3^( - 9 )⁶ ] =

3¹⁸ : [ 3^( - 9 × 6 ) ] =

3¹⁸ : [ 3^( - 54 ) ] =

3^[ 18 - ( - 54 ) ] =

3^72