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?(1 point)

Question

Responses

1/5^22
Start Fraction 1 over 5 superscript 22 baseline end fraction

1/5^4
Start Fraction 1 over 5 superscript 4 baseline end fraction

5^9/5^−13
Start Fraction 5 superscript 9 baseline over 5 superscript negative 13 baseline End Fraction

5^4

Answer 1

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

So, we combine the exponents: \[ 5^9 \cdot 5^{-13} = 5^{9 + (-13)} = 5^{-4} \]

To write this expression with only positive exponents, we can use the property \( a^{-m} = \frac{1}{a^m} \): \[ 5^{-4} = \frac{1}{5^4} \]

Among the options given, the equivalent expression using only positive exponents is: \[ \frac{1}{5^4} \]

Thus, the correct response is: 1/5^4.