To simplify the expression \( 13^{-5} \cdot 13^{-11} \) using the properties of exponents, we can apply the rule that states when multiplying two expressions with the same base, we add the exponents:
\[ a^m \cdot a^n = a^{m+n} \]
Applying this to our expression, we have:
\[ 13^{-5} \cdot 13^{-11} = 13^{-5 + (-11)} = 13^{-16} \]
Now, to express this with only positive exponents, we rewrite \( 13^{-16} \) as:
\[ 13^{-16} = \frac{1}{13^{16}} \]
Thus, the equivalent expression with positive exponents is:
\[ \frac{1}{13^{16}} \]
Looking at the given options, the correct answer is:
Start Fraction 1 over 13 superscript 16 baseline end fraction.
1 answer