Simplify (7×13)^13 ÷ (13×7)^17: Power Operations with Equal Bases

The question requires us to simplify the given expression using the laws of exponents, specifically the Power of a Quotient Rule for Exponents. The given expression is:

$\frac{\left(7\times13\right)^{13}}{\left(13\times7\right)^{17}}$

We can rewrite the expression inside both the numerator and the denominator to express them more clearly:

$\left(7\times13\right)^{13} = (91)^{13}$ and $\left(13\times7\right)^{17} = (91)^{17}$

The expression now looks like this:

$\frac{(91)^{13}}{(91)^{17}}$

According to the properties of exponents, specifically the rule for dividing same bases, we subtract the exponents:

$(91)^{13-17} = (91)^{-4}$

The expression now simplified is:

$\frac{1}{(91)^4}$

Therefore, we see that the simplified answer does not directly correspond to the given answer of "a' + b' = c'." It seems there might be a discrepancy in the final simplification or understanding, as we derived:

The solution to the question is: $\frac{1}{(91)^4}$

I couldn't get to the shown answer, "a'+b' are correct."