Question

simplify








pls help to solve





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Answer 1

SOLUTION

TO SIMPLIFY

$\sf{ {[ {3}^{ - 1} \times {4}^{ - 1} ]}^{ - 1} \times {6}^{ - 1} }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on indices that :

‌

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

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

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

$\sf{4. \: \: {(ab)}^{m} = {a}^{m} \times {b}^{m} }$

‌$\displaystyle \sf{5. \: \: {a}^{0} = 1}$

EVALUATION

PROCESS : 1

$\sf{ {[ {3}^{ - 1} \times {4}^{ - 1} ]}^{ - 1} \times {6}^{ - 1} }$

$\sf{ = [ {({3}^{ - 1})}^{ - 1} \times {({4}^{ - 1})}^{ - 1} ] \times {6}^{ - 1} } \: \: \: ( \:By \: formula \: 4 \: )$

$\sf{ = [ {({3}^{ })}^{ - 1 \times - 1} \times {({4}^{ })}^{ - 1 \times - 1} ] \times {6}^{ - 1} }$

$\sf{ = [ 3 \times 4] \times {6}^{ - 1} }$

$\ \sf{ = 12 \times \dfrac{1}{6} }$

$\ \sf{ = 2}$

PROCESS : 2

$\sf{ {[ {3}^{ - 1} \times {4}^{ - 1} ]}^{ - 1} \times {6}^{ - 1} }$

$\displaystyle \sf{ = { \bigg[ \frac{1}{3} \times \frac{1}{4} \bigg ]}^{ - 1} \times {6}^{ - 1} }$

$\displaystyle \sf{ = { \bigg[ \frac{1}{12} \bigg ]}^{ - 1} \times {6}^{ - 1} }$

$\displaystyle \sf{ = { \bigg[ {12}^{ - 1} \bigg ]}^{ - 1} \times {6}^{ - 1} }$

$\displaystyle \sf{ = { \bigg[ {12}^{ } \bigg ]}^{ - 1 \times - 1} \times {6}^{ - 1} }$

$\displaystyle \sf{ = { \bigg[ {12}^{ } \bigg ]}^{ 1} \times {6}^{ - 1} }$

$\displaystyle \sf{ =12 \times \frac{1}{6} }$

$\displaystyle \sf{ = 2}$

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