Question

8. Evaluate the (Don't spam)_If you then your 10 answer will be reported_​

Answer 1

Here is your answer mate in the attached picture

If you feel it's correct pls mark it as brainliest.

Answer 2

8. Evaluate

• $\sf(i) \: \dfrac{4}{ ({216)^{ \frac{ - 2}{3} } } } + \dfrac{1}{ ({256)^{ \frac{ - 3}{4} } } } + \dfrac{2}{ ({243)^{ \frac{ - 1}{5} } } }$

Solution

$\sf \: \: \implies \: \: \dfrac{4}{ ({216)^{ \frac{ - 2}{3} } } } + \dfrac{1}{ ({256)^{ \frac{ - 3}{4} } } } + \dfrac{2}{ ({243)^{ \frac{ - 1}{5} } } }$

$\sf \: \: \implies \: \: \dfrac{4}{ ({6 \times 6 \times 6)^{ \frac{ - 2}{3} } } } + \dfrac{1}{ ({4 \times 4 \times 4 \times 4)^{ \frac{ - 3}{4} } } } + \dfrac{2}{ ({3 \times 3 \times 3 \times 3 \times 3)^{ \frac{ - 1}{5} } } }$

$\sf \: \: \implies \: \: \dfrac{4}{ ({ {6}^{3} )^{ \frac{ - 2}{3} } } } + \dfrac{1}{ ({ {4}^{4} )^{ \frac{ - 3}{4} } } } + \dfrac{2}{ ({ {3}^{5} )^{ \frac{ - 1}{5} } } }$

$\sf \: \: \implies \: \: \dfrac{4}{ ({ {6} )^{3 \times \frac{ - 2}{3} } } } + \dfrac{1}{ ({ {4} )^{ 4 \times \frac{ - 3}{4} } } } + \dfrac{2}{ ({ {3})^{5 \times \frac{ - 1}{5} } } }$

$\sf \: \: \implies \: \: \dfrac{4}{ ({ {6} )^{ - 2 } } } + \dfrac{1}{ ({ {4} )^{ - 3 } } } + \dfrac{2}{ ({ {3})^{ - 1 } } }$

$\sf \: \: \implies \: \: \dfrac{4}{ { \dfrac{1}{ {6}^{2} } } } + \dfrac{1}{ { \dfrac{1}{ {4}^{3} } } } + \dfrac{2}{ { \dfrac{1}{3} } }$

$\sf \: \: \implies \: \: \dfrac{4}{ { \dfrac{1}{ 36} } } + \dfrac{1}{ { \dfrac{1}{ 64 } } } + \dfrac{2}{ { \dfrac{1}{3} } }$

$\sf \: \: \implies \: \: 4 \times 36 + 64 + 2 \times 3$

$\sf \: \: \implies \: \: 144 + 64 + 6$

$\sf \: \: \implies \: \: 144 + 70$

$\bf \: \: \implies \: \: 214$

More to know (◠‿◕)

$\\\begin{gathered}\begin{gathered}\\\\\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \bigstar \: \underline{\bf{}}\\ {\boxed{\begin{array}{c | c} \frac{ \: ~~~~~~~~~~\: \: \: \: \:\sf Laws \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{ } &\frac{ \: ~~~~~~~~~~ \: \: \: \: \:\sf Example \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{ }\\ \sf \bigstar{a}^{m} \times {a}^{n} = {a}^{m + n} & \sf {a}^{2} \times {a}^{3} = {a}^{2 + 3} = {a}^{6} \\ \\ \sf \bigstar{a}^{m} \div {a}^{n} = {a}^{m - n}& \sf {a}^{3} \div {a}^{2} = {a}^{3 - 2} = {a}^{1} \\ \\ \sf{\bigstar \: \: \: \: \: \: ( {a}^{m} ) ^{n} = {a}^{mn} } & \sf( {a}^{2} ) ^{3} = {a}^{2 \times 3} = {a}^{6} \\ \\ {\bigstar\sf a {}^{m} \times {n}^{m} = (ab) ^{m} } &\sf a {}^{2} \times {b}^{2} = (ab) ^{2}\\ \\ \sf\bigstar \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {a}^{0} = 1& \sf {2}^{0} = 1 \: \: \: \: \\ \\ \sf \bigstar \: \: \: \: {\dfrac{ {a}^{m} }{ {b}^{m} }= \left( \dfrac{a}{b} \right) ^{m} }& \sf{\dfrac{ {a}^{2} }{ {b}^{2} }= \left( \dfrac{a}{b} \right) ^{2} }\\\\\bigstar~~~~~~~ \sf x^{\frac{m}{n} }=\sqrt[n]{x^m}\sf = (\sqrt[n]{x})^m & \sf x^{\frac{2}{3} }=\sqrt[3]{x^2} = (\sqrt[n]{x})^m\\ \\\\ \end{array}}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$