Expressing 729 as a power of 3

Expressing a number as a power of another number is a way to represent it in a simplified form. In this case, we want to express 729 as a power of 3. Let's break down the process step by step.

Step 1: Understand the concept
To express a number as a power of another number, we need to find the exponent (power) to which the base number needs to be raised to obtain the given number.

Step 2: Prime factorization of 729
To find the prime factorization of 729, we divide it by prime numbers until we can no longer divide it evenly. The prime factorization of 729 is:

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

So, the prime factorization of 729 is 3 × 3 × 3 × 3 × 3 × 3, which can be written as 3^6.

Step 3: Expressing 729 as a power of 3
Now that we know the prime factorization of 729, we can express it as a power of 3. Since 729 is equal to 3^6, we can write:

729 = 3^6

In other words, 729 can be expressed as the number 3 raised to the power of 6.

Conclusion
So, 729 can be expressed as 3^6, which means it is equal to the number 3 raised to the power of 6. This representation allows us to simplify and understand the number 729 in terms of its relationship to the base number 3.

From a rectangular piece of mental sheet of length and breadth 1.60m and 80 cm respectively, 3 circular sheets of 20 cm radius are cut out. What area of metal is left ? Use π=3.14.