Fill in the blanks to make the statements true.

729 = 3^—

We know that 729 is the cube of 9

729 = 9³

We also know that square of 3 = 9

So 729 = (3²)³

According to the law of indices:

(a^m)ⁿ = a^{(m × n)}

Applying the same law here,

In the above question,

a = 3

m = 2

n = 3

∴ m × n = 2 × 3

= 6

So 729 = 3⁶

Therefore the answer for the fill in the blanks = 6