Question

How many multiples of $9^3$ are greater than $9^4$ and less than $9^5$?

Answer 1

To find the multiples of $9^3$ that are greater than $9^4$ and less than $9^5$, we need to consider the powers of 9 in that range. There are six multiples that satisfy the given condition.

Step-by-step explanation:

To find out how many multiples of $9^3$ are greater than $9^4$ and less than $9^5$, we need to consider the powers of 9 in that range. $9^3$ is equal to $729$ and $9^4$ is equal to $6561$. To determine the multiples, we need to find the integers that can be obtained by multiplying $729$ by an integer greater than $1$ and less than $9$.

Since $729 = 9 imes 81$, the multiples of $9^3$ are $729, 1458, 2187, 2916, 3645, 4374, 5103, 5832$. Out of these, the multiples that are greater than $9^4$ and less than $9^5$ are $1458, 2187, 2916, 3645, 4374, 5103$. Therefore, there are six multiples of $9^3$ that satisfy the given condition.

Answer 2

The number of multiples of 729 that are greater than 6561 and less than 59049 is 72

How many multiples of 9³ are greater than 9⁴ and less than 9⁵?

`{9}^(3) = 729`

`{9}^(4) = 6561`

`{9}^(5) = 59049`

Number of multiples of 729 that are greater than 6561 and less than 59049 can be determined by finding the difference between the multiples of 729 in 59049 and multiples of 729 in 6561

= (multiples of 729 in 59049) - (multiples of 729 in 6561)

= 81 - 9

= 72

Hence, there are 72 multiples of 9³ between 9⁴ and 9⁵