Question

Express 6561 as a power of a prime number.

• A. $3^6$
• B. $9^4$
• C. $3^9$
• D. $3^8$

Answer 1

The correct option is D $3^8$

Sum of digits of 6561 = 6+5+6+1 = 18.
As 18 is divisible by 3, 6561 is also divisible by 3.

6561 can be expressed as a power of 3 as 3 is the only prime number which is a factor of 6561.

6561 ÷ 3 = 2187
2187 ÷ 3 = 729
729 ÷ 3 = 243
243 ÷ 3 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9÷3 = 3
3÷3 =1

6561 can be written as (3×3×3×3×3×3×3×3)
So, 6561 = $3^8$