Class 9 Math All topics Number Systems

Simplify:

(i) $2_{23}2_{51}$ (ii) $(3_{3}1 )_{7}$ (iii) $11_{41}11_{21} $ (iv) $7_{21}⋅8_{21}$

Solution:

(i) $2_{23}.2_{51}$

By using property $X_{a}$. $X_{b}$=$X_{a+b}$

$=2_{23+51}=2_{1017}$

(ii) $(3_{3}1 )_{7}$

By using property $(yx )_{a}=y_{b}x_{a} $

$=(3_{3})_{7}1 $

$=3_{21}1 $ ...... $[∵(x_{a})_{b}=x_{ab}]$

(iii) $11_{41}11_{21} $

By using property $X_{b}X_{a} =X_{a−b}$

$=11_{21−41}=11_{41}$

(iv) $7_{21}.8_{21}$

$=56_{21}$ ...... $[∵x_{a}y_{a}=(xy)_{a}]$

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introduction to trigonometry

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