Question

find the value of the following q 5 and 6​

Answer 1

Answer:

v)

$( {5}^{ - 1} \times {3}^{ - 1} )^{ - 1} \div {6}^{ - 1} \\ = ( \frac{1}{5} \times \frac{1}{3})^{ - 1} \div {6}^{ - 1} \\ = (\frac{1 \times 1}{3 \times 5} ) ^{ - 1} \div {6}^{ - 1} \\ = ( \frac{1}{15} ) ^{ - 1} \div {6}^{ - 1} \\ = ( {15}^{ - 1} )^{ - 1} \div {6}^{ - 1} \\ = ({15}^{ - 1 \times - 1} ) \div {6}^{ - 1} \\ = {15}^{1} \div \frac{1}{6} \\ = 15 \times 6 \\ = 90$

Hence the answer is 90.

vi)

$( {6}^{ - 1} - {8}^{ - 1} )^{ - 1} \div ( {2}^{ - 1} - {3}^{ - 1})^{ - 1} \\ = (\frac{1}{6} - \frac{1}{8} )^{ - 1} \div ( \frac{1}{2} - \frac{1}{3} )^{ - 1} \\ (lcm \: of \: 6 \: and \: 8 \: is \: 48. \: and \: lcm \: of \: 2 \: and \: 3 \: is \: 6. \\ = ( \frac{(1 \times 8) - (1 \times 6)}{48} )^{ - 1} \div ( \frac{(1 \times 3) - (1 \times 2)}{6} )^{ - 1} \\ = ( \frac{8 - 6}{48} )^{ - 1} \div (\frac{3 - 2}{6} )^{ - 1} \\ = ( \frac{2}{48} )^{ - 1} \div ( \frac{1}{6} )^{ - 1} \\ = ( \frac{2 \div 2}{48 \div 2})^{ - 1} \div ( {6}^{ - 1} )^{ - 1} \\ = ( \frac{1}{24} )^{ - 1} \div {6}^{ - 1 \times - 1} \\ = ( {24}^{ - 1} )^{ - 1} \div {6}^{1} \\ = {24}^{ - 1 \times - 1} \div 6 \\ = 24 \div 6 \\ = 4$

Hence the answer is 4.

hope it helps.