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WAEC Mathematics 2023 Paper

Question : 14

Total: 50

Solve

2^{5x} \div 2^x = \;\sqrt[5]{2^{10}}

Solution:

Concept:

Use the laws of indices:

\;a^m \div a^n = a^{m-n}

and

\;\sqrt[n]{a^m} = a^{\frac{m}{n}}

Explanation:

Rewrite the left side using the division rule for exponents.

2^{5x} \div 2^x = 2^{5x - x} = 2^{4x}

Now rewrite the right side, the fifth root of

2^{10}

\sqrt[5]{2^{10}} = 2^{\frac{10}{5}} = 2^2

The equation becomes:

2^{4x} = 2^2

Since the bases are equal, equate the powers.

4x = 2

Divide both sides by 4:

x = \frac{2}{4} = \frac{1}{2}

Answer:

x = \frac{1}{2}

, which is option B.

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