Which of the following is an equivalent expression to 59⋅5−13

Question

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

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

154
Start Fraction 1 over 5 superscript 4 baseline end fraction

54
5 superscript 4 baseline

1522

Answer 1

To simplify the expression \(59 \cdot 5^{-13}\) using the properties of integer exponents and to express it with positive exponents, we can apply the property that states \(a^m \cdot a^n = a^{m+n}\).

Here, we have:

\[ 59 \cdot 5^{-13} = 5^{9} \cdot 5^{-13} \]

Using the property mentioned above:

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

Since we want an expression with only positive exponents, we can rewrite \(5^{-4}\) as:

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

Now we can match with the provided options. The equivalent expression with positive exponents is:

\(\frac{1}{5^4}\)

So, the correct response is:

Start Fraction 1 over 5 superscript 4 baseline end fraction