Solve the Nested Fraction: 2/(8·(4/(3·(10/(4·8)))) Step-by-Step

First, we will start with the innermost parentheses, we rewrite the expression in fraction form:

$2/(8\cdot(4/(3\cdot\frac{10}{4\times8})))=$

We add the 3 to the numerator of the fraction and create a multiplication expression:

$2/(8\cdot(4/(\frac{3\times10}{4\times8})))=$

Again, we address the innermost parentheses, we invert the fraction to create a multiplication expression:

$2/(8\cdot(4\times\frac{4\times8}{3\times10}))=$

We add the 4 to the numerator of the fraction and create a multiplication exercise:

$2/(8\cdot\frac{4\times4\times8}{3\times10})=$

We add the 8 to the numerator of the fraction and create a multiplication exercise:

$2:\frac{8\times4\times4\times8}{3\times10}=$

Now we will invert the fraction to create a multiplication exercise:

$2\times\frac{3\times10}{8\times4\times4\times8}=$

We add the 2 to the numerator of the fraction and create a multiplication exercise:

$\frac{2\times3\times10}{8\times4\times4\times8}=$

We break down the 10 in the numerator and the 4 in the denominator into smaller multiplication exercises:

$\frac{2\times3\times2\times5}{8\times2\times2\times4\times8}=$

We simplify to 2 in the numerator and denominator:

$\frac{3\times5}{8\times4\times8}=$

We solve the multiplication exercises in the numerator and denominator from left to right:

$\frac{3\times5}{8\times4\times8}=\frac{15}{32\times8}=\frac{15}{256}$