S i m p l i f y space semicolon space fraction numerator 6 to the power of begin display style 2 over 3 end style end exponent x cube root of 6 to the power of 7 end root over denominator cube root of 6 to the power of 6 end root end fraction

Asked by kishor.kp14 | 21st Jun, 2019, 01:55: PM

Expert Answer:

begin mathsize 16px style fraction numerator 6 to the power of begin display style 2 over 3 end style end exponent cross times cube root of 6 to the power of 7 end root space to the power of space space end exponent over denominator cube root of 6 to the power of 6 end root end fraction
equals space fraction numerator 6 to the power of 2 over 3 end exponent cross times open parentheses 6 close parentheses to the power of 1 third cross times 7 end exponent over denominator begin display style open parentheses 6 close parentheses to the power of fraction numerator begin display style 1 end style over denominator begin display style 3 end style end fraction cross times 6 end exponent end style end fraction space space space space space space space space space space space space space space space space... space since space open parentheses straight a to the power of straight m close parentheses to the power of straight n space equals space straight a to the power of mn
equals fraction numerator begin display style 6 to the power of fraction numerator begin display style 2 end style over denominator begin display style 3 end style end fraction end exponent cross times open parentheses 6 close parentheses to the power of fraction numerator begin display style 7 end style over denominator begin display style 3 end style end fraction end exponent end style over denominator begin display style open parentheses 6 close parentheses squared end style end fraction
equals 6 to the power of fraction numerator begin display style 2 end style over denominator begin display style 3 end style end fraction plus fraction numerator begin display style 7 end style over denominator begin display style 3 end style end fraction space end exponent over 6 squared space space space space space space space space space space space space space space space space space space space space space space... space since space straight a to the power of straight m cross times space straight a to the power of straight n space equals space straight a to the power of straight m plus space straight n end exponent
equals 6 to the power of begin display style 9 over 3 end style end exponent over 6 squared equals fraction numerator begin display style 6 cubed end style over denominator 6 squared end fraction equals 6 to the power of 3 space minus space 2 end exponent equals space 6 to the power of 1 equals 6 space space space space space space space space space space space space space... space since space straight a to the power of straight m divided by straight a to the power of straight n space equals space straight a to the power of straight m minus space straight n end exponent
end style

Answered by Yasmeen Khan | 21st Jun, 2019, 04:54: PM