Question

simplify : {(2/13)^-6/(2/13)^3}^3*(2/13)-9
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Answer 1

(13/2)¹⁸

Simplification:

The given equation is = $\frac{\frac{2}{13} ^{-6} }{\frac{2}{13} ^{-3}} ^{3} \frac{2}{13} ^{-9}$ --------------- (i)

As we know that,

aᵇ x aⁿ = a⁽ᵇ⁺ⁿ⁾     ----- (ii)

and, aᵇ / aⁿ = a⁽ᵇ⁻ⁿ⁾    ----- (iii)

Applying rule (iii) in (i)

= ((2/13)⁻⁶⁺³)³ 2/13⁻⁹

= ((2/13)⁻³)³ 2/13⁻⁹

Applying rule (ii) in (i)

= (2/13)⁻⁹ 2/13⁻⁹

= (2/13)⁻⁹⁻⁹

= (2/13)⁻¹⁸

= (13/2)¹⁸

Hence, the final answer after simplifying $\frac{\frac{2}{13} ^{-6} }{\frac{2}{13} ^{-3}} ^{3} \frac{2}{13} ^{-9}$ is (13/2)¹⁸.