Question

simplify and write the answer in exponential form​

Answer 1

Step-by-step explanation:

using identities formula,

${a}^{ - m} = \frac{1}{ {a}^{m} }$

$({6}^{ - 4} \div {6}^{ - 3}) \times {(\frac{6}{7}})^{3} \times {6}^{ - 2}$

$= ( \frac{1}{{6}^{4}} \div \frac{1}{{6}^{3}} ) \times {(\frac{6}{7}})^{3} \times { \frac{1}{6}^{2}} \\ \\ = ( \frac{1}{{6}^{4}} \ \times \ \: {{6}^{3}} ) \times {(\frac{6}{7}})^{3} \times { { (\frac{1}{6})}^{2} }$

$= \frac{1 \times {6}^{3} \times {6}^{3} \: \times 1 }{ {6}^{4} \times {7}^{3} \times {6}^{2} } \\ \\ = \frac{ {6}^{3 + 3} }{ {6}^{4 + 2} \times {7}^{3}}$

$= \frac{ {6}^{6} }{ {6}^{6} \times {7}^{3} } = \frac{1}{ {7}^{3} } \\ \\ = \frac{1}{343}$