Which of the following is an equivalent expression to 5^9 x 5^−13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?

Answer 1

To find an equivalent expression with positive exponents, we can apply the properties of integer exponents.

According to the property $a^m \cdot a^n = a^{m+n}$, we can combine the two exponents of 5 by adding them together.

Thus, $5^9 \cdot 5^{-13} = 5^{9 + (-13)} = 5^{-4}$.

To convert the negative exponent to a positive exponent, we can use the property $a^{-n} = \dfrac{1}{a^n}$.

Therefore, $5^{-4} = \dfrac{1}{5^4}$.

The equivalent expression with only positive exponents is $\boxed{\dfrac{1}{5^4}}$.