Question

(42:14)^2 x 9^18 : 27^6

Answer 1

42:14=3

9¹⁸=(3²)¹⁸=3²ˣ¹⁸=3³⁶

27⁶=(3³)⁶=3³ˣ⁶=3¹⁸

3²x3³⁶:3¹⁸=3²⁺³⁶⁻¹⁸=3^20

aⁿ*aᵇ=aⁿ⁺ᵇ

aⁿ:aᵇ=aⁿ⁻ᵇ

(aⁿ)ᵇ=aⁿˣᵇ

Answer 2

$(42 : 14) ^{2} \times {9}^{18} : {27}^{6} = \\ \\ {(42 : 14)}^{2} \times { {(3}^{2}) }^{18} : { {(3}^{3}) }^{6} = \\ \\ {(42 : 14)}^{2} \times {3}^{2 \times 18} \div {3}^{3 \times 6} = \\ \\ {(42 : 14)}^{2} \times {3}^{36} : {3}^{18} = \\ \\ {(42 : 14)}^{2} \times {3}^{18} = \\ \\ {3}^{2} \times {3}^{18} = \\ \\ {3}^{2 + 18} = \\ \\ {3}^{20}$