What is the result of the operation 1 / 16,807 multiplied by 1 / 2,401?

To find the result of the operation ( \frac{1}{16807} \times \frac{1}{2401} ), we first multiply the two fractions together. When multiplying fractions, you multiply the numerators and the denominators:

[ \frac{1 \times 1}{16807 \times 2401}

]

Next, we need to evaluate the product of the denominators, ( 16807 ) and ( 2401 ). Both of these numbers are powers of ( 7 ):

( 16807 = 7^5 ) and ( 2401 = 7^4 ).

When you multiply these together:

[ 16807 \times 2401 = 7^5 \times 7^4 = 7^{5+4} = 7^9 ]

Thus, we have:

[ \frac{1}{16807 \times 2401} = \frac{1}{7^9} ]

This tells us that the operation results in:

[ \frac{1}{7^9} ]

Now, if we evaluate the choices presented, ( \frac{1}{49} ) is