Simplify the Fraction: (4³)/(5³×7³) Step-by-Step Solution

To solve this problem, we will apply the rule for powers of a quotient. By recognizing that the expression $\frac{4^3}{5^3 \times 7^3}$ can be seen in terms of powers, we can reformulate it:

$\frac{4^3}{5^3 \times 7^3} = \frac{4^3}{(5 \times 7)^3}$

Now, we see this as a single fraction raised to the same power, which can be expressed using the power of a fraction rule:

$\frac{4^3}{(5 \times 7)^3} = \left(\frac{4}{5 \times 7}\right)^3$

Thus, the expression given is equivalent to

$\left(\frac{4}{5 \times 7}\right)^3$.