Simplify: \;{27^{m+1}}{3^{m+2}}

Correct Answer is : 32m+13²m+1}32m+1

Correct Answer is : 32m+13²m+1}32m+1

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BECE Mathematics 2024 Paper

Question : 20

Total: 40

Simplify:

\;\frac{27^{m+1}}{3^{m+2}}

Solution:

Concept:

Use the laws of indices to express both terms in the same base, then simplify the exponents.

Explanation:

Write

27

as a power of

3

27 = 3^3

So,

27^{m+1} = (3^3)^{m+1}

Apply the power rule:

(a^m)^n = a^{mn}

(3^3)^{m+1} = 3^{3(m+1)} = 3^{3m+3}

Now, rewrite the fraction:

\frac{27^{m+1}}{3^{m+2}} = \frac{3^{3m+3}}{3^{m+2}}

Use the division rule:

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

= 3^{(3m+3)-(m+2)}

= 3^{3m+3-m-2}

= 3^{2m+1}

Answer:

3^{2m+1}

So, the correct option is D.

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