Simplify:\({\left[ {{{\left( {\frac{{216}}{{64}}} \right)}^{\frac{2}{3}\;}} \times {{\left( {\frac{{256}}{{81}}} \right)}^{ - \frac{1}{4}}} \div {{\left( {\frac{{16}}{{144}}} \right)}^{

Simplify:\({\left[ {{{\left( {\frac{{216}}{{64}}} \right)}^{\frac{2}{3}\;}} \times {{\left( {\frac{{256}}{{81}}} \right)}^{ - \frac{1}{4}}} \div {{\left( {\frac{{16}}{{144}}} \right)}^{ - \frac{1}{2}}}} \right]^{\frac{1}{2}}}\)

A 3/4

B 2/5

C 1/4

D 1/5

E None of these

Solution

Correct Answer: Option A

Laws of indices:

(a^m)ⁿ = a^{m × n}

a^m × aⁿ = a^m+n

a^m ÷ aⁿ = a^m

\({\left[ {{{\left( {\frac{{216}}{{64}}} \right)}^{2/3\;}} \times {{\left( {\frac{{256}}{{81}}} \right)}^{ - 1/4}} \div {{\left( {\frac{{16}}{{144}}} \right)}^{ - 1/2}}} \right]^{1/2}}\)

\(= {\left[ {{{\left( {\frac{{216}}{{64}}} \right)}^{2/3\;}} \times {{\left( {\frac{{81}}{{256}}} \right)}^{1/4}} \times {{\left( {\frac{{16}}{{144}}} \right)}^{1/2}}} \right]^{1/2}}^\;\)

\(= {\left[ {\frac{{36}}{{16}} \times \frac{3}{4} \times \frac{4}{{12}}} \right]^{1/2}}{\;^\;}\)

\(= {\left( {\frac{9}{{16}}} \right)^{\frac{1}{2}}}^\;\)

= (3/4)

Solution

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