If A = (243)^{0.12} × (243)^{0.08} and \(B = {\left( {\frac{1}{{216}}} \right)^{ - \frac{2}{3}}} \div {\left( {\frac{1}{{27}}} \right)^{ - \frac{4}{3}}}\) then what is the value of B/A?

This question was previously asked in

DSSSB PRT General Section Official Paper - 13 Nov 2019 Shift 1

Option 2 : 4/27

Given:

A = (243)0.12 × (243)0.08

\(B = {\left( {\frac{1}{{216}}} \right)^{ - \frac{2}{3}}} \div {\left( {\frac{1}{{27}}} \right)^{ - \frac{4}{3}}}\)

Calculation:

A = (243)0.12 × (243)0.08

A = (243)^{(0.12 + 0.08)}

A = (243)^{0.2}

A = (3^{5})^{1/5}

A = 3

\(B = {\left( {\frac{1}{{216}}} \right)^{ - \frac{2}{3}}} \div {\left( {\frac{1}{{27}}} \right)^{ - \frac{4}{3}}}\)

\(B = {\left( {\frac{1}{{6^3}}} \right)^{ - \frac{2}{3}}} \div {\left( {\frac{1}{{3^3}}} \right)^{ - \frac{4}{3}}}\)

\(B = {\left( {\frac{1}{{6}}} \right)^{3 \times- \frac{2}{3}}} \div {\left( {\frac{1}{{3}}} \right)^{3 \times- \frac{4}{3}}}\)

\(B = {\left( {\frac{1}{{6}}} \right)^{- {2}}} \div {\left( {\frac{1}{{3}}} \right)^{{-4}}}\)

\(B = {\left( {{{6}}} \right)^{{2}}} \div {\left( {{3}} \right)^{{4}}}\)

\(B = {\left( {{{36}}} \right)} \div {\left( {{81}} \right)}\)

\(B = \frac{4}{9}\)

Now;

\(\frac{B}{A} = \frac {\frac{4}{9}}{3}\)

\(\frac{B}{A} = \frac {4}{27}\)

Hence, **option (2) **is the correct answer.