Question

How to express 729 as a power of 3

Answer 1

To express 729 as a power of 3 is $3^{6}.$

Step-by-step explanation:

We have,

729

To express 729 as a power of 3 = ?

∴ 729

$=27\times 27$

$=3\times 3 \times 3 \times 3 \times 3\times 3$

$=3^{1} \times 3^{1}\times 3^{1} \times 3^{1} \times 3^{1} \times 3^{1}$

$=3^{1+1+1+1+1+1}$

Using the identity,

$a^{m} \times b^{n}\times c^{0} \times ......=a^{m+n+o+.....}$

$=3^{6}$

Hence, to express 729 as a power of 3 is $3^{6}.$

Answer 2

Given:

A number 729.

To Find:

The number 729as powers of 3.

Solution:

The given problem can be solved using the concepts of prime factorization.

1. Prime factorization of a number implies converting a number into the product of prime factors.

2. The number 729 can be also written as,

=> 729 = 3 x 243,

=> 729 = 3 x 3 x 81,

=> 729 = 3 x 3 x 3 x 27,

=> 729 = 3 x 3 x 3 x 3 x 9,

=> 729 = 3 x 3 x 3 x 3 x 3 x 3.

=> 729 =$3^6$.

3. Hence the power form of 729 is $3^6$.

Therefore, the number 729 as a power of 3 is written as$3^6$.