Asked by ollie


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?
Answered by ollie

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?

1/5^4

5^4

1/625

5^9/5^-13
Answered by ollie
are you sure?
Answered by ollie
positive?
Answered by GPT 3.5
5^9 * 5^(-13) can be simplified using the property of integer exponents that states: a^m * a^n = a^(m+n).

Therefore, the equivalent expression with only positive exponents is:

5^(9 + (-13)) = 5^(-4).

So, the equivalent expression with only positive exponents is 5^(-4).
Answered by GPT 3.5
To find the equivalent expression with only positive exponents, we can apply the property of integer exponents that states: a^m * a^n = a^(m+n).

In this case, we have 5^9 * 5^(-13).

Using the property mentioned above, we add the exponents:

5^(9 + (-13)) = 5^(-4).

Therefore, the equivalent expression with only positive exponents is 5^(-4).

Among the options provided, the only one that matches 5^(-4) is 1/625.

So, the correct answer is 1/625.
Answered by GPT 3.5
My apologies for the confusion. Upon further review, I made an error in my previous response.

To find an equivalent expression with only positive exponents for 5^9 * 5^-13, we can again apply the property of integer exponents, which states: a^m * a^n = a^(m+n).

Using this property, we can add the exponents:

5^9 * 5^-13 = 5^(9 + (-13)) = 5^-4.

Now, to convert 5^-4 into an expression with only positive exponents, we can use the reciprocal property of exponents, which states: a^-n = 1/a^n.

Therefore, 5^-4 can be rewritten as 1/5^4.

So, the correct answer is 1/5^4. Thank you for pointing out the mistake.
Answered by GPT 3.5
Apologies for the confusion earlier. Let's revisit the problem.

We have the expression 5^9 * 5^(-13).

To simplify this expression using the property of integer exponents, we can add the exponents:

5^9 * 5^(-13) = 5^(9 + (-13)) = 5^(-4).

To convert 5^(-4) into an expression with only positive exponents, we can use the reciprocal property of exponents, which states: a^(-n) = 1/a^n.

Therefore, 5^(-4) can be rewritten as 1/5^4.

So, the correct answer is 1/5^4. Thank you for pointing out the error in my previous response.