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BECE Mathematics 2012 Paper

Question : 8

Total: 40

Simplify

\;\frac{5^7 \times 5^4}{5^2}

Solution:

Concept:

Use the laws of indices for multiplication and division of powers with the same base.

Explanation:

When multiplying powers with the same base, add the exponents:

a^m \times a^n = a^{m+n}

So,

5^7 \times 5^4 = 5^{7+4} = 5^{11}

Now divide by

5^2

. When dividing powers with the same base, subtract the exponents:

\frac{a^m}{a^n} = a^{m-n}

Therefore,

\frac{5^{11}}{5^2} = 5^{11-2} = 5^9

Answer:

5^9

, which is option C.

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