Correct Answer - Option 2 : 2/9
To solve questions of this type, follow the laws of “Surds and indices’’ given below-
Laws of Indices:-
\(1 - :\;{a^m} \times {a^n} = {a^{\left\{ {m + n} \right\}}}\)
\(2 - :\;{a^m} \div {a^n} = {a^{\left\{ {m - n} \right\}}}\)
\(3 - :\;{\left( {{a^m}} \right)^n} = {a^{mn}}\)
\(4 - :{\left( a \right)^{ - m}} = \frac{1}{{{a^m}}}\)
\(5 - :{\left( a \right)^{\frac{m}{n}}} = \sqrt[n]{{{a^m}}}\)
\(6 - :{\left( a \right)^0} = 1\)
Calculations:
44 × (24)2 ÷ (83 × 32 × 43)
\(⇒ {2^8} \times \frac{{{2^8}}}{{{2^9} \times {3^2} \times {2^6}}}\)
\(⇒ \frac{{{2^{8 + 8 - 9 - 6}}}}{{{3^2}}}\)
⇒ 2/9
∴ The correct answer is 2/9
