Simplify 8ⁿ x 2²n} + 4³n}

Correct Answer is : 2−n^{-n}−n

Correct Answer is : 2−n^{-n}−n

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WAEC Further Mathematics 2025 Paper

Question : 21

Total: 40

Simplify 8

^n

^{2n}

^{3n}

Solution:

Concept:

Use the laws of indices by expressing every base as a power of 2.

Explanation:

Write each term with base 2:

8^n = (2^3)^n = 2^{3n}

2^{2n}

stays unchanged.

4^{3n} = (2^2)^{3n} = 2^{6n}

So the expression becomes

\frac{2^{3n} \times 2^{2n}}{2^{6n}}

Combine the powers in the numerator using the multiplication rule:

2^{3n} \times 2^{2n} = 2^{3n+2n} = 2^{5n}

Now divide by

2^{6n}

2^{5n} \div 2^{6n} = 2^{5n-6n}

This simplifies to

2^{-n}

Answer:

2^{-n}

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