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?

Question

Responses

5^4

1/5^4

1/625

5^9/5^−13

Answer 1

To simplify the expression and apply the properties of integer exponents, we can add the exponents when multiplying and subtract the exponents when dividing.

In this case, when we multiply two powers with the same base, we add the exponents. So, 5^9 * 5^(-13) simplifies to 5^(9+(-13)), which is equal to 5^(-4).

When we have a negative exponent, we can rewrite it as the reciprocal of the base raised to the positive exponent. So, 5^(-4) is equivalent to 1/5^4.

Therefore, the equivalent expression with positive exponents is 1/5^4.

So, the correct answer is 1/5^4.