Answer:
The given such number is 6.
Step-by-step explanation:
Let the given such number = m
Now, according to the question, the given expression is:
[tex]\frac{(m^{12}) }{(m^{9}) } = 216[/tex]
By the LAW OF EXPONENTS:
[tex]\frac{x^a}{x^b} = x^{(a-b)}[/tex]
⇒Here [tex]\frac{m^{12}}{m^9} = m^{(12-9)} = m^{(3)}[/tex]
or, the given expression becomes [tex]m^3 = 216\\\implies m = \sqrt[3]{216} = 6[/tex]
or, m = 6
Hence, the given such number is 6.
