Question

121raise to power n ×1331²=11 raise to power 9 . Find the value of n.

Answer 1

Answer:

VERIFIED ANSWER ✓✓✓

Step-by-step explanation:

The answer is

n ≈ ³/ ²

Answer 2

Answer:

required value of n is 4.

Step-by-step explanation:

Given,121 raise to power n ×1331²=11 raise to power 9

${121}^{n} \times {1331}^{2} = {11}^{9}$

Here we want to find value of n.

By prime factorisation,

$121 = 11 \times 11 = {11}^{2}$

$1331 = 11 \times 11 \times 11 = {11}^{3}$

So,

${121}^{n} \times {1331}^{2} = {11}^{9} \\ { ({11}^{2}) }^{n} \times {11}^{3} = {11}^{9} \\ {11}^{2n} \times 11 = {11}^{9} \\ {11}^{2n + 1} = {11}^{9} \\ 2n + 1 = 9 \\ 2n = 9 - 1 \\ 2n = 8 \\ n = \frac{8}{2} \\ n = 4$

Therefore required value of n is 4.

Here applied formulas,

${x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ if \: {x}^{a} = {x}^{b} \: then \: a = b$

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