Which of the following is an equivalent expression to 59⋅5−13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)

Question

Responses

1522
Start Fraction 1 over 5 superscript 22 baseline end fraction

154
Start Fraction 1 over 5 superscript 4 baseline end fraction

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

54

Answer 1

To find an equivalent expression to \(59 \cdot 5^{-13}\) with only positive exponents, we can apply the Properties of Integer Exponents.

1. First, we know that \(5^{-13}\) can be rewritten using positive exponents: \[ 5^{-13} = \frac{1}{5^{13}} \]

2. Now substituting this back into the expression gives: \[ 59 \cdot 5^{-13} = 59 \cdot \frac{1}{5^{13}} = \frac{59}{5^{13}} \]

3. Next, applying the exponent rule \(\frac{a^m}{a^n} = a^{m-n}\) we can combine them:

   • In this case, we have \(5^9 \cdot 5^{-13}\) which equals: \[ = 5^{9 - 13} = 5^{-4} = \frac{1}{5^4} \]

Now let's analyze the responses provided:

• 1522 (not relevant to the expression we derived)
• Start Fraction 1 over 5 superscript 22 baseline end Fraction (not relevant)
• Start Fraction 1 over 5 superscript 4 baseline end Fraction (this is equivalent to \(5^{-4}\))
• 595−13 (is a reformulation of the original expression but not with only positive exponents)
• 54 (not relevant)

The expression that is equivalent to \(59 \cdot 5^{-13}\) and has only positive exponents is:

Start Fraction 1 over 5 superscript 4 baseline end Fraction.