Question

5^3+5^3+5^3+5^3+5^3=5^n
Find n

Answer 1

5³ + 5³ + 5³ + 5³ + 5³ = 5ⁿ

taking 5³ as common,

5³(1+1+1+1+1) = 5ⁿ

5³(5) = 5ⁿ

$5 = \frac{ {5}^{n} }{ {5}^{3} }$

$we \: know \: that \: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

$5 = {5}^{n - 3}$

5 can be written as 5¹

${5}^{1} = {5}^{n - 3}$

taking the powers alone,

1 = n - 3

1 + 3 = n

4 = n

Hope it helps!!

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