To solve the equation \( \frac{5^6}{5^2} = a^b \), we can simplify the left side first.
Using the property of exponents that states \( \frac{x^m}{x^n} = x^{m-n} \), we can simplify \( \frac{5^6}{5^2} \):
\[ \frac{5^6}{5^2} = 5^{6-2} = 5^4 \]
So now we have:
\[ 5^4 = a^b \]
Next, to express \( a \) in terms of \( 5 \), we can assume \( a = 5 \). Therefore, we can substitute \( a \) into the equation:
\[ 5^4 = (5)^b \]
Since the bases are the same, we can set the exponents equal to each other:
\[ 4 = b \]
Thus, the value of \( b \) is:
\[ \boxed{4} \]
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