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Question : 11 of 86

Marks: +1, -0

If

\;\frac{(243)^{\frac{n}{5}} \times 3^{2n+1}}{9^{n} \times 3^{n-1}}=x

, then the value of

x

is:

1
3
9
$3^{n}$

Solution:

Concept:

Simplify using laws of indices: express all terms as powers of 3.

Explanation:

Write

243 = 3^5

, so

(243)^{\frac{n}{5}} = (3^5)^{\frac{n}{5}} = 3^n

.

Write

9^n = (3^2)^n = 3^{2n}

.

The numerator becomes

3^n \cdot 3^{2n+1} = 3^{n+2n+1} = 3^{3n+1}

.

The denominator becomes

3^{2n} \cdot 3^{n-1} = 3^{2n+n-1} = 3^{3n-1}

.

Thus

x = \frac{3^{3n+1}}{3^{3n-1}} = 3^{(3n+1)-(3n-1)} = 3^{2} = 9

.

Answer:

x = 9

, which corresponds to option C.

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