Question

*(3/5)⁻² = ?*
1️⃣ 3/5
2️⃣ -3/5
3️⃣ 25/9
4️⃣ -9/25
​

Answer 1

Answer:

25/9 is the right answer

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

$\displaystyle \sf{ { \bigg( \frac{3}{5} \bigg)}^{ - 2} } =$

$\displaystyle \sf{1. \: \: \frac{3}{5} }$

$\displaystyle \sf{ 2. \: \: - \frac{3}{5} }$

$\displaystyle \sf{3. \: \: \frac{25}{9} }$

$\displaystyle \sf{ 4. \: \: - \frac{9}{25} }$

FORMULA TO BE IMPLEMENTED

‌We are aware of the formula on indices that :

‌

‌$\sf{1. \: \: {a}^{m} \times {a}^{n} = {a}^{m + n} }$

‌$\displaystyle \sf{2. \: \: \: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }$

‌$\displaystyle \sf{3. \: \: \: { ({a}^{m} )}^{n} = {a}^{mn} }$

‌$\displaystyle \sf{4. \: \: {a}^{0} = 1}$

‌

EVALUATION

Here the given expression is

$\displaystyle \sf{ { \bigg( \frac{3}{5} \bigg)}^{ - 2} }$

We simplify it as below

$\displaystyle \sf{ { \bigg( \frac{3}{5} \bigg)}^{ - 2} }$

$\displaystyle \sf{ = { \bigg[ \bigg( \frac{5}{3} \bigg) {}^{ - 1} \bigg] }^{ - 2} }$

$\displaystyle \sf{ = { \bigg[ \bigg( \frac{5}{3} \bigg) {}^{} \bigg] }^{ (- 2) \times (- 1)} }$

$\displaystyle \sf{ = { \bigg( \frac{5}{3} \bigg) {}^{} }^{2} }$

$\displaystyle \sf{ = \frac{25}{9} }$

FINAL ANSWER

Hence the correct option is

$\displaystyle \sf{ 3. \: \: \frac{25}{9} }$

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