Simplify and express each of the following in exponential form:
${(- 7)}^{3} \div [{(- 7)}^{6} \times {(- 7)}^{5}]$

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Solution

Given that ,
${(- 7)}^{3} \div [{(- 7)}^{6} \times {(- 7)}^{5}] = {(- 7)}^{3} \div {(- 7)}^{6 + 5} = {(- 7)}^{3} \div {(- 7)}^{11} = \frac{{(- 7)}^{3}}{{(- 7)}^{11}} = {(- 7)}^{3} \times {(- 7)}^{- 11} = {(- 7)}^{3 - 11} = {(- 7)}^{- 8}$ ; [ Using law of exponent : $a^{n} \times a^{m} = a^{m + n}$ and $a^{- n} = \frac{1}{a^{n}}$ ]
Hence , the required value is ${(- 7)}^{- 8}$ .

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