Question

$how \: {5}^{k} + 4. {5}^{k} \: change \: into \: {5}^{k \: + \: 1}$
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Answer 1

It's not 4.5^k it's actually written 4 × 5^k

So we know a^m + a^n = a^(m+n)

therefore, 5^k + 5^1 = 5^k+1