Q. 7^55 + 7^55 + 7^55 + 7^55 + 7^55 + 7^55 + 7^55 = ?

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Q. 7⁵⁵ + 7⁵⁵ + 7⁵⁵ + 7⁵⁵ + 7⁵⁵ + 7⁵⁵ + 7⁵⁵ = ?

Given:

        7⁵⁵+7⁵⁵+7⁵⁵+7⁵⁵+7⁵⁵+7⁵⁵+7⁵⁵

There are 7 identical terms.

Factor out =7×7⁵⁵

Apply law of exponents : a^m×aⁿ=a^m+ⁿ

So,

        7×7⁵⁵=7¹⁺⁵⁵=7⁵⁶

Ans: 756

Quick Trick:

Same power repeated k times ⇒ aⁿ+aⁿ+…(k times) = k⋅aⁿ = aⁿ+log_a^k 

For base same and k also equals base: Here, k = 7 (same as base 7)
So just add the exponent: 7⁵⁵×7¹=7⁵⁶