Question

guys please help need answer within 5 minutes. I will mark brainliest.​

Answer 1

$⟹ {({ (\frac{2}{3}) }^{2} )}^{3} \times {( \frac{1}{3} )}^{ - 4} \times {(3)}^{ - 1} \times \frac{1}{6}$

To simplify the above expression first use the identity :-

$⟹ {({ (a) }^{m} )}^{n} = {a}^{mn}$

$⟹ { (\frac{2}{3}) }^{6} \times {( \frac{1}{3} )}^{ - 4} \times {(3)}^{ - 1} \times \frac{1}{6}$

Now use :-

$⟹ { (a) }^{ - m} = \frac{1}{{a}^{m}}$

$⟹ { (\frac{2}{3}) }^{6} \times {( \frac{3}{1} )}^{ 4} \times \frac{1}{3} \times \frac{1}{6}$

$⟹ \frac{ {(2)}^{6} \times {3}^{4} \times 1 }{ {3}^{6} \times 3 \times 3 \times 2 }$

Now use :-

${a}^{m} {a}^{n} = {a}^{m + n}$

$⟹ \frac{ {(2)}^{6} \times {3}^{4} \times 1 }{ {3}^{8} \times 2 }$

Now use :-

$\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

$⟹ {(2)}^{6 - 1} \times {(3)}^{4 - 8}$

$⟹ {(2)}^{5} \times {(3)}^{ - 4 }$

$⟹ \frac{{(2)}^{5}}{{(3)}^{ 4 }}$

$⟹ \frac{32}{81}$

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Learn more:-

$1)a^m × a^n= {a}^{(m + n)}$

$2) {( {a}^{m})}^{n}  = {a}^{mn}$

$3) {ab}^{n} = {a}^{n} {b}^{n}$

$4) \frac{ {(a)}^{m} }{ {(a)}^{n} } = {a}^{m - n}$

$5) {a}^{ - b} = \frac{1}{ {a}^{b} }$