Question

Please answer the following question :-
(7/3)^-3 * (9/7)^-2 * (3/7) using the formulas
Its from the chapter Exponents and Powers

Please answer it fast!!
Its very urgent!!
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Answer 1

Identities used :

${( \frac{a}{b}) }^{ - m} = {( \frac{b}{a} )}^{ m} \\ \\ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} \\ \\ {a}^{m} \times {a}^{n} = {a}^{m + n}$

Now,

${( \frac{7}{3} )}^{ - 3} \times {( \frac{9}{7} )}^{ - 2} \times {( \frac{3}{7} )} \\ \\ = {( \frac{3}{7} )}^{3} \times {( \frac{7}{ {(3)}^{2} } )}^{2} \times \frac{3}{7} \\ \\ = \frac{ {3}^{3} }{ {7}^{3} } \times \frac{ {7}^{2} }{ {( {3}^{2} )}^{2} } \times \frac{3}{7} \\ \\ = \frac{ {3}^{3} \times {7}^{2} \times 3 }{ {7}^{3} \times {3}^{4} \times 7} \\ \\ = \frac{ {3}^{3 + 1} \times {7}^{2} }{ {3}^{4} \times {7}^{3 + 1} } \\ \\ = {3}^{4 - 4} \times {7}^{2 - 4} \\ \\ = {3}^{0} \times {7}^{ - 2} \\ \\ = \frac{1}{ {7}^{2} } \\ \\ = \frac{1}{49}$