To simplify the expression \( 13^{-6} \div 13 \div 13^{-2} \), we can first rewrite the divisions as multiplications by the reciprocal:
\[ 13^{-6} \div 13 = 13^{-6} \cdot 13^{-1} \]
Now, using the rule for multiplying powers with the same base (which states that you add the exponents), we get:
\[ 13^{-6} \cdot 13^{-1} = 13^{-6 + (-1)} = 13^{-7} \]
Next, we need to divide by \( 13^{-2} \):
\[ 13^{-7} \div 13^{-2} = 13^{-7} \cdot 13^{2} \]
Again, we apply the rule for multiplying powers with the same base:
\[ 13^{-7} \cdot 13^{2} = 13^{-7 + 2} = 13^{-5} \]
To express the final answer in exponential form with positive exponents only, we rewrite \( 13^{-5} \) as:
\[ \frac{1}{13^5} \]
Thus, the fully simplified expression is:
\[ \frac{1}{13^5} \]
1 answer