Simplify the Expression: (6^5)/(13^5×4^5) Step by Step

To solve this problem, we aim to rewrite the given expression using the properties of exponents. The expression we need to deal with is $\frac{6^5}{13^5 \times 4^5}$.

We can simplify this using the formula for powers of fractions, which states that if two exponents are the same, we can treat the fraction as a whole raised to that exponent: $\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m$.

Applying this to the problem, considering the expression $\frac{6^5}{(13 \times 4)^5}$ all raised to the power of 5 can be rewritten, using our formula, as a single fraction raised to the same power:
$\left(\frac{6}{13 \times 4}\right)^5$.

This simplifies the entire expression to a clear fraction raised to the power 5. Therefore, the corresponding expression to the original problem is:

$\left(\frac{6}{13 \times 4}\right)^5$.