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ICSE Class 9 Answered

Q22
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Asked by pankaj.shukla2 | 30 Sep, 2018, 05:23: AM
answered-by-expert Expert Answer
begin mathsize 16px style fraction numerator open parentheses begin display style 1 over 9 end style close parentheses to the power of 2 straight y minus 1 end exponent open parentheses 0.0081 close parentheses to the power of begin display style 1 third end style end exponent over denominator square root of 243 end fraction equals open parentheses 1 third close parentheses to the power of 2 straight y minus 5 end exponent cube root of fraction numerator begin display style 27 to the power of straight y minus 1 end exponent end style over denominator begin display style 10000 end style end fraction end root
rightwards double arrow fraction numerator begin display style open parentheses 1 over 3 squared close parentheses to the power of 2 straight y minus 1 end exponent open parentheses 0.3 to the power of 4 close parentheses to the power of 1 third end exponent end style over denominator square root of 3 to the power of 5 end root end fraction equals open parentheses 3 to the power of negative 1 end exponent close parentheses to the power of 2 straight y minus 5 end exponent cube root of fraction numerator begin display style 3 to the power of 3 left parenthesis end exponent to the power of straight y minus 1 right parenthesis end exponent end style over denominator begin display style 10 to the power of 4 end style end fraction end root
rightwards double arrow fraction numerator 3 to the power of negative 2 open parentheses 2 straight y minus 1 close parentheses end exponent cross times open parentheses begin display style 3 over 10 end style close parentheses to the power of begin display style 4 over 3 end style end exponent over denominator 3 to the power of begin display style 5 over 2 end style end exponent end fraction equals 3 to the power of negative 2 straight y plus 5 end exponent cross times 3 to the power of begin display style fraction numerator 3 open parentheses straight y minus 1 close parentheses over denominator 3 end fraction end style end exponent over 10 to the power of begin display style 4 over 3 end style end exponent
rightwards double arrow 3 to the power of negative 4 straight y plus 2 plus fraction numerator begin display style 4 end style over denominator begin display style 3 end style end fraction minus fraction numerator begin display style 5 end style over denominator begin display style 2 end style end fraction end exponent cross times 10 to the power of fraction numerator negative 4 over denominator 3 end fraction end exponent equals 3 to the power of negative 2 straight y plus 5 plus straight y minus 1 end exponent cross times 10 to the power of fraction numerator negative 4 over denominator 3 end fraction end exponent
rightwards double arrow negative 4 straight y plus 2 plus fraction numerator begin display style 4 end style over denominator begin display style 3 end style end fraction minus fraction numerator begin display style 5 end style over denominator begin display style 2 end style end fraction equals negative 2 straight y plus 5 plus straight y minus 1
rightwards double arrow negative 4 straight y plus 5 over 6 equals negative straight y plus 4
rightwards double arrow negative 3 straight y equals 4 minus fraction numerator begin display style 5 end style over denominator begin display style 6 end style end fraction
rightwards double arrow negative 3 straight y equals 19 over 6
rightwards double arrow straight y equals fraction numerator negative 19 over denominator 18 end fraction end style
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