Wich of the following is an equivalent to 5^9×5^-13 with only positive exponents that has been generated by applying the properties of integer exponents
5^9/5^-13
1/625
5^4
1/5^4
To simplify the expression 5^9 × 5^-13, we can apply the rule of exponents that states:
a^m × a^n = a^(m+n).
Using this rule, we can add the exponents together:
5^9 × 5^-13 = 5^(9 + (-13)).
Since adding a positive number and a negative number is the same as subtracting their absolute values, we can simplify further:
5^9 × 5^-13 = 5^(-4).
Therefore, the equivalent expression with only positive exponents is 5^(-4), which can also be written as 1/5^4.
So, the correct answer is 1/5^4.