(3/8) to the power -2 * (4/5) to the power -3

Asked by samruddhikhedkar85.8spicertl | 2nd Jun, 2020, 09:36: PM

Expert Answer:

begin mathsize 16px style open parentheses 3 over 8 close parentheses to the power of negative 2 end exponent cross times open parentheses 4 over 5 close parentheses to the power of negative 3 end exponent
equals 1 over open parentheses 3 over 8 close parentheses squared cross times 1 over open parentheses 4 over 5 close parentheses cubed space space space....... straight a to the power of negative straight m end exponent equals 1 over straight a to the power of straight m
equals 8 squared over 3 squared cross times 5 cubed over 4 cubed
equals fraction numerator 4 squared cross times 2 squared over denominator 3 squared end fraction cross times 5 cubed over 4 cubed
equals fraction numerator 4 squared cross times 4 to the power of negative 3 end exponent cross times 2 squared cross times 5 cubed over denominator 3 squared end fraction
equals fraction numerator 4 to the power of 2 minus 3 end exponent cross times 2 squared cross times 5 cubed over denominator 3 squared end fraction space space....... straight a to the power of straight m cross times straight a to the power of straight n equals straight a to the power of straight m plus straight n end exponent
equals fraction numerator 2 squared cross times 5 cubed over denominator 2 squared cross times 3 squared end fraction
equals 125 over 9 end style

Answered by Yasmeen Khan | 3rd Jun, 2020, 09:06: AM