Which of the following is an equivalent expression to $$ 5^{9} \cdot 5^{-13} $$ with only positive exponents that has been generated by applying the Properties of Integer Exponents? (1 point) $$ \frac{1}{5^{4}} $$ $$ \frac{1}{5^{4}} $$ $$ \frac{5^{9}}{5^{-13}} $$

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$$\frac{1}{5^{4}}$$ To simplify the expression $$ 5^{9} \cdot 5^{-13} $$ using the properties of integer exponents, we can apply the property that states $$ a^m \cdot a^n = a^{m+n} $$. So, we have: $$ 5^{9} \cdot 5^{-13} = 5^{9 + (-13)} = 5^{9 - 13} = 5^{-4} $$ Now, to express $$ 5^{-4} $$ with only positive exponents, we can use the property that $$ a^{-n} = \frac{1}{a^n} $$: $$ 5^{-4} = \frac{1}{5^{4}} $$ Thus, the equivalent expression to $$ 5^{9} \cdot 5^{-13} $$ with only positive exponents is: $$ \frac{1}{5^{4}} $$ Therefore, the correct answer is: $$\frac{1}{5^{4}}$$

Which of the following is an equivalent expression to \( 5^{9} \cdot 5^{-13} \) with only positive exponents that has been generated by applying the Properties of Integer Exponents? (1 point) \( \frac{1}{5^{4}} \) \( \frac{1}{5^{4}} \) \( \frac{5^{9}}{5^{-13}} \)

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Which of the following is an equivalent expression to \( 5^{9} \cdot 5^{-13} \) with only positive exponents that has been generated by applying the Properties of Integer Exponents? (1 point) \( \frac{1}{5^{4}} \) \( \frac{1}{5^{4}} \) \( \frac{5^{9}}{5^{-13}} \)

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