Question

If `(5^m xx 5^3 xx 5^-2)/5^-5 = 5^12`, find m.

Answer 1

Given, `(5^m xx 5^3 xx 5^-2)/5^-5 = 5^12`

Using laws of exponents,

a^m + aⁿ = (a)^{m – n} and `a^-m = 1/a^n`  ...[∵ a is non-zero integer]

Then, 5^m × 5³ × 5^–2 × 5⁵ = 5¹²

⇒ 5^m × 5⁸ × 5^–2 = 5¹²

⇒ 5^m × 5⁶ = 5¹²

⇒ 5^{m + 6} = 15¹²  ...[∵ a^m × aⁿ = a^{m + n}]

On comparing both sides, we get

m + 6 = 12

⇒ m = 6