# Extra Questions For CBSE Class 9 Maths Chapter 1 | Q7

###### Number System | Rules of exponents & indices

Question 7: Simplify and find the value of
(a) ${$729)}^{$frac{1}{6}})$b) ${$64)}^{$frac{2}{3}})$c) ${$243)}^{$frac{6}{5}})$d) ${$21)}^{$frac{3}{2}} × {$21)}^{$frac{5}{2}})$e) $$frac{{$81$}^{$frac{1}{3}}}{{$81)}^{$frac{1}{12}}}) ## Target Centum in CBSE 10th Maths #### Free Online CBSE Coaching online.maxtute.com ### Video Explanation ## NCERT Solution to Class 10 Maths #### With Videos ### Explanatory Answer | Number Systems Extra Questions ####$a) ${$729)}^{$frac{1}{6}}) Prime factorize 729 = 3 × 3 × 3 × 3 × 3 × 3 = 36 ${$729$}^{$frac{1}{6}}) = ${$3^6)}^{1/6}$ = (3)(6/6) = 3
Rule of exponents used: ${(a^x)}^{y}$ = axy

#### (b) ${$64)}^{$frac{2}{3}}) Prime factorize 64 = 2 × 2 × 2 × 2 × 2 × 2 = 26 ${$64$}^{$frac{2}{3}}) = ${$2^6)}^{2/3}$ = (2)(12/3) = (2)4 = 16
Rule of exponents used: ${(a^x)}^{y}$ = axy

#### (c) ${$243)}^{$frac{6}{5}}) Prime factorize 243 = 3 * 3 * 3 * 3 * 3 = 35 ${$243$}^{$frac{6}{5}}) = ${$3^5)}^{6/5}$ = 36 = 729
Rule of exponents used: ${(a^x)}^{y}$ = axy

#### (e) $$frac{{$81$}^{$frac{1}{3}}}{{$81)}^{$frac{1}{12}}}) $\frac{{$81$}^{$frac{1}{3}}}{{$81)}^{$frac{1}{12}}}) = ${$81$}^{$frac{1}{3} - $frac{1}{12}}$ = ${$81$}^{$frac{{4-1}}{12}}) = ${$81$}^{$frac{3}{12}}) = ${$81$}^{$frac{1}{4}}) Prime factorize 81 = 3 × 3 × 3 × 3 = 34 ${$81$}^{$frac{1}{4}}) = ${${3^4}$}^{$frac{1}{4}}) = ${$3$}^{$frac{4}{4}}$ = 3
Rule of exponents used: $\frac{a^x}{a^y}$ = ax – y

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