Question

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Answer 1

Given  :2^(n) - 2^(n - 1) = 4.

⇒ 2^n - 2^(-1) * 2^n

⇒ 2^n(1 - 2^-1) = 4

⇒ 2^n(1 - 1/2) = 4

⇒ 2^n(1/2) = 4

⇒ 2^n = 8

⇒ 2^n = 2^3

⇒ n = 3.

Therefore:

⇒ n^n

⇒ 3^3

⇒ 27.

Hope it helps!

Answer 2

${(2)}^{n} - {(2)}^{n - 1} = 4 \\ \\ = > {(2)}^{n} - \frac{ {(2)}^{n} }{ {(2)}^{1} } = 4 \\ \\ = > {(2)}^{n} \times (1 - \frac{1}{2} ) = 4 \: \: \: \: \: \: (taking \: {(2)}^{n} as \: common) \\ \\ = > {(2)}^{n} \times ( \frac{2 - 1}{2} ) = 4 \\ \\ = > {(2)}^{n} \times \frac{1}{2} = 4 \\ \\ = > {(2)}^{n} = 4 \times \frac{2}{1} \\ \\ = > {(2)}^{n} = 8 \\ \\ = > {(2)}^{n} = {(2)}^{3} \: \\ \\ now \: same \: bases \: \\ equating \: their \: powers \\ \\ = > n = 3$

The value of n = 3.

To be found :

${(n)}^{n} = {(3)}^{3} = 3 \times 3 \times 3 = 27$

Hence, the value of $\ {(n)}^{n}$ is 27.