Simplify \(8^{n} \times 2^{2n} \div 4^{3n}\)

Assessment: WAEC SSCE - Further Mathematics - 2006 (Objective) Subject: Further Mathematics

Question 1 Report

Simplify \(8^{n} \times 2^{2n} \div 4^{3n}\)

Answer Details
We can simplify the expression by first rewriting each of the bases as powers of 2: $$8^{n} \times 2^{2n} \div 4^{3n} = (2^{3})^{n} \times 2^{2n} \div (2^{2})^{3n}.$$ Using the laws of exponents, we can simplify this to: $$(2^{3n}) \times 2^{2n} \div 2^{6n} = 2^{3n+2n-6n} = 2^{-n}.$$ Therefore, the simplified expression is \(2^{-n}\).
Read lesson note on Indices And Logarithmic Functions (WAEC)
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