Given that2025= {3}^(k * ) {5}^(t) state the values of k and t​

Question

Given that2025=

`{3}^(k * ) {5}^(t)`
state the values of k and t​

Answer 1

k = 4, t = 2

Explanation:

Express 2025 as a product of its prime factors

2025 =
`3^(4)` × 5², that is

`3^(4)` × 5² =
`3^(k)` ×
`5^(t)`

Comparing exponents of same bases on both sides, gives

k = 4 and t = 2