Solve the Nested Division Problem: 75:(8:(4:15))

First, we rewrite the multiplication exercise within the inner parentheses as a fraction:

$75:(8:\frac{4}{15})=$

Now we invert the fraction to create a multiplication exercise:

$75:(8\times\frac{15}{4})=$

We add the 8 to the numerator of the fraction in the multiplication exercise:

$75:\frac{8\times15}{4}=$

Now we invert the fraction to create a multiplication exercise:

$75\times\frac{4}{8\times15}=$

We add the 75 to the numerator of the fraction in the multiplication exercise:

$\frac{75\times4}{8\times15}=$

We break down the 75 and the 8 into smaller multiplication exercises:

$\frac{15\times5\times4}{4\times2\times15}=$

We simplify the 4 and the 15 in the numerator and denominator:

$\frac{5}{2}=2\frac{1}{2}$