Represent the following mixed infinite decimal periodic fractions as common fractions:
$(\frac{3}{\sqrt{1 + a}} + \sqrt{1 - a}) : (\frac{3}{\sqrt{1 - a^{2}}} + 1)$

Question

Represent the following mixed infinite decimal periodic fractions as common fractions-displaystyleleft - frac-1-3- right -10- cdot 27-3- - 0-2-4- cdot 25-2- - -64-1-9-3-

Toppr Admin · Accepted Answer

-3-10-3-3-x2212-3- -102-4-125-2-12-9-19-x2212-3-xA0- -xA0- -xA0- -by using the property of x-x2212-1-1x- and vice varsa-3-10-3-x2212-9-1000016-125-2-2-3-3-10-x2212-9-1-83-1-8-12-

Represent the following mixed infinite decimal periodic fractions as common fractions:
${(\frac{1}{3})}^{- 10} \cdot 27^{- 3} + {0.2}^{- 4} \cdot 25^{- 2} + (64^{- 1 / 9})^{- 3}$

$(3)^{10} . ((3)^{3})^{- 3} +$ $(\frac{10}{2})^{4}$ $(\frac{1}{25})^{2}$ + $(((\frac{1}{2})^{9})^{\frac{1}{9}})^{- 3}$ {by using the property of $x^{- 1} = \frac{1}{x}$ } and vice varsa
$(3)^{10} . (3)^{- 9} + \frac{10000}{16} . (\frac{1}{25})^{2} + (2)^{3}$
$(3)^{10 - 9} + 1 + 8$
$3 + 1 + 8 = 12.$

Represent the following mixed infinite decimal periodic fractions as common fractions:(13)−10⋅27−3+0.2−4⋅25−2+(64−1/9)−3

(3)10.((3)3)−3+ (102)4(125)2+(((12)9)19)−3 {by using the property of x−1=1x} and vice varsa(3)10.(3)−9+1000016.(125)2+(2)3(3)10−9+1+83+1+8=12.

Represent the following mixed infinite decimal periodic fractions as common fractions:
${(\frac{1}{3})}^{- 10} \cdot 27^{- 3} + {0.2}^{- 4} \cdot 25^{- 2} + (64^{- 1 / 9})^{- 3}$

$(3)^{10} . ((3)^{3})^{- 3} +$ $(\frac{10}{2})^{4}$ $(\frac{1}{25})^{2}$ + $(((\frac{1}{2})^{9})^{\frac{1}{9}})^{- 3}$ {by using the property of $x^{- 1} = \frac{1}{x}$ } and vice varsa
$(3)^{10} . (3)^{- 9} + \frac{10000}{16} . (\frac{1}{25})^{2} + (2)^{3}$
$(3)^{10 - 9} + 1 + 8$
$3 + 1 + 8 = 12.$