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

595−13
Start Fraction 5 superscript 9 baseline over 5 superscript negative 13 baseline End Fraction

1522
Start Fraction 1 over 5 superscript 22 baseline end fraction

54
5 superscript 4 baseline

1/5^4

Answer 1

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

Thus, we have:

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

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

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

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

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

Among the provided options, the correct response is:

1/5^4.