Simplify:-44 × (24)2 ÷ (83 × 32 × 43)1. 4/92. 2/93. 84. 8/3

1.	Simplify:-44 × (24)2 ÷ (83 × 32 × 43)1. 4/92. 2/93. 84. 8/3
Answer» 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

Answer» 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

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