Question

How many times of 30 must be added together to get a sum equal to 30⁷?

Answer 1

Let n be the number of times that 30 must be added together to get a sum equal to 30⁷

Therefore, we can write that `ubrace(30 + 30 + .... + 30)_("n times") = 30^7`

⇒ 30 × n = 30⁷  ...`[∵ ubrace(a + a + ... + a)_("n times") = a xx n]`

⇒ `(30 xx n)/30 = 30^7/30`  ...[Dividing both sides by 30]

⇒ n = 30^{7 – 1}  ...`[∵ a^m/a^n = a^(m - n)]`

∴ n = 30⁶

Hence, if 30 is added 30⁶ times, then, then we get 30⁷.