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JAMB Mathematics 2019 Paper

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Question : 34

Total: 73

Simplify 81

^{-\frac{3}{4}}

^{\frac{1}{2}}

^{\frac{2}{5}}

$\frac{2}{5}$
$\frac{3}{5}$
$\frac{5}{2}$
$\frac{5}{3}$

Solution:

Concept:

Use the laws of indices to simplify powers with the same base before multiplying.

Explanation:

Write each number as a power of its prime base.

81 = 3^4

,

25 = 5^2

, and

243 = 3^5

.

Apply the power law:

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

.

81^{-\frac{3}{4}} = (3^4)^{-\frac{3}{4}} = 3^{-3} = \frac{1}{27}

.

25^{\frac{1}{2}} = (5^2)^{\frac{1}{2}} = 5^1 = 5

.

243^{\frac{2}{5}} = (3^5)^{\frac{2}{5}} = 3^2 = 9

.

Now combine the simplified values.

\frac{1}{27} \times 5 \times 9 = \frac{45}{27}

.

Reduce the fraction:

\frac{45}{27} = \frac{5}{3}

.

Answer:

D.

\frac{5}{3}

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