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)
Responses
1\5^4
5^4
5^9\5^−13
1\625
The equivalent expression that has only positive exponents and has been generated by applying the properties of integer exponents is 1/625.
To simplify the expression 5^9⋅5^−13 with only positive exponents using the Properties of Integer Exponents, we can add the exponents.
So, 5^9⋅5^−13 = 5^(9 + -13)
Since a negative exponent represents the reciprocal of the base raised to the positive exponent, we have:
5^(-13) = 1/5^13
Therefore, the equivalent expression with only positive exponents is 5^(9 + -13) = 5^(-4) = 1/5^4.
So, the correct choice from the given options is:
1. 5^4