Question

{(3/2)^4}^-2
please solve the questions immediately
so I will mark you brainlist ​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

SOLUTION

TO SIMPLIFY

$\displaystyle \sf \bigg \{{ \bigg({ \frac{3}{2 } \bigg)}^{4} \bigg \}}^{ - 2}$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on indices that :

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

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

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

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

$\displaystyle \sf 5. \: \: \: \bigg({ \frac{a}{b} \bigg)}^{n} = \frac{ {a}^{n} }{ {b}^{n} }$

$\displaystyle \sf 6. \: \: \: {a}^{ - m} = \frac{1}{ {a}^{m} }$

EVALUATION

Here the given expression is

$\displaystyle \sf \bigg \{{ \bigg({ \frac{3}{2 } \bigg)}^{4} \bigg \}}^{ - 2}$

We simplify it as below

$\displaystyle \sf \bigg \{{ \bigg({ \frac{3}{2 } \bigg)}^{4} \bigg \}}^{ - 2}$

$\displaystyle \sf = \bigg({ \frac{3}{2 } \bigg)}^{4 \times ( - 2)} \: \: \: \: \: (Using \: Formula \: 3)$

$\displaystyle \sf = \bigg({ \frac{3}{2 } \bigg)}^{ - 8}$

$\displaystyle \sf = \frac{1}{\big({ \frac{3}{2 } \big)}^{ 8} } \: \: \: \: \: (Using \: Formula \: 6)$

$\displaystyle \sf = {\bigg({ \frac{2}{3 } \bigg)}^{ 8} }$

$\displaystyle \sf = \frac{ {2}^{8} }{ {3}^{8} } \: \: \: \: \: (Using \: Formula \: 5)$

$\displaystyle \sf = \frac{256}{6561}$

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