Question

Question

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

Answer 1

To simplify the expression \( 5^9 \cdot 5^{-13} \) using the properties of integer exponents, we can apply the property which states that \( a^m \cdot a^n = a^{m+n} \).

1. Combine the exponents: \[ 5^9 \cdot 5^{-13} = 5^{9 + (-13)} = 5^{9 - 13} = 5^{-4} \]

2. Rewrite \( 5^{-4} \) with a positive exponent: \[ 5^{-4} = \frac{1}{5^4} \]

Thus, the equivalent expression to \( 5^9 \cdot 5^{-13} \) with only positive exponents is: \[ \frac{1}{5^4} \]