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BECE Mathematics 2023 Paper

Question : 38

Total: 40

Simplify:

\;\frac{5^7 \times 5^{-4}}{5^3}

Solution:

Concept:

Use the laws of exponents to combine powers with the same base.

Explanation:

First, apply the multiplication rule:

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

So,

5^7 \times 5^{-4} = 5^{7 + (-4)} = 5^{3}

Now the expression becomes

\frac{5^3}{5^3}

Apply the division rule:

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

Thus,

\frac{5^3}{5^3} = 5^{3-3} = 5^0

Any non-zero number raised to the power zero equals

1

, so

5^0 = 1

Therefore, the simplified value is

1

Answer:

1

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