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)
1/5^4
To simplify the expression 5^9 * 5^-13 and rewrite it with only positive exponents, we can use the properties of integer exponents.
The property we can apply is:
a^m * a^n = a^(m+n)
Applying this property to our expression, we get:
5^9 * 5^-13 = 5^(9 + (-13))
Since adding a positive number with a negative number gives us a negative number, the exponent becomes negative:
5^(9 + (-13)) = 5^(-4)
Thus, an equivalent expression with only positive exponents is 5^(-4).
To find an equivalent expression with positive exponents, we can use the properties of integer exponents. The property that will be useful in this case is the negative exponent property, which states that any term raised to a negative exponent can be moved to the denominator and become positive. The expression 5^9 * 5^-13 can be rewritten as:
5^9 * 1/5^13
Using this property, we moved 5^-13 to the denominator and changed its exponent to positive. Now, to simplify further, we can combine the like bases, which in this case is 5:
5^9 * 1/5^13 = 5^(9-13) = 5^-4
So, the equivalent expression with positive exponents that has been generated by applying the properties of integer exponents is 5^-4.