Which of the following is an equivalent expression to 5^9⋅5^−13

Question

with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses

Answer 1

To simplify the expression \( 5^9 \cdot 5^{-13} \), we can apply the properties of exponents. According to the property \( a^m \cdot a^n = a^{m+n} \), we can combine the exponents:

\[ 5^9 \cdot 5^{-13} = 5^{9 + (-13)} = 5^{9 - 13} = 5^{-4} \]

Now, to express \( 5^{-4} \) with only positive exponents, we can use the property that states \( a^{-n} = \frac{1}{a^n} \):

\[ 5^{-4} = \frac{1}{5^4} \]

Therefore, the equivalent expression with only positive exponents for \( 5^9 \cdot 5^{-13} \) is:

\[ \frac{1}{5^4} \]