Question

A number to the 12th power divided by the same number to the 9th power equals 216. What is the number?

Answer 1

The given such number is 6.

Explanation:

Let the given such number = m

Now, according to the question, the given expression is:

`((m^(12)) )/((m^(9)) )   =  216`

By the LAW OF EXPONENTS:

`(x^a)/(x^b)  = x^((a-b))`

⇒Here
`(m^(12))/(m^9)  = m^((12-9))  = m^((3))`

or, the given expression becomes
`m^3 =  216\\\implies m = \sqrt[3]{216}  = 6`

or, m = 6

Hence, the given such number is 6.