Which of the following is an equivalent expression to 5^9 x 5^-13 with only positive exponents that has been generated by applying the properties of integers exponents
5^-4
To simplify the expression 5^9 x 5^-13 and obtain an equivalent expression with only positive exponents, you can use the properties of integer exponents.
First, recall that the property states: a^m x a^n = a^(m+n).
Using this property, we can rewrite the expression as:
5^9 x 5^-13 = 5^(9+(-13))
Since 9 + (-13) is equivalent to -4, the expression becomes:
5^(9+(-13)) = 5^(-4)
However, we want an equivalent expression with only positive exponents. To achieve that, we can use another property of integer exponents: a^(-n) = 1/a^n.
Applying this property to 5^(-4), we get:
5^(-4) = 1/(5^4)
Therefore, the equivalent expression with only positive exponents is:
1/(5^4)
To find an equivalent expression with only positive exponents, we can use the properties of integer exponents.
The property we'll use here is that when we multiply powers with the same base, we add the exponents.
The given expression is 5^9 * 5^-13. Using the property mentioned earlier, we can rewrite this expression as 5^(9 + (-13)).
To solve the exponent inside the parentheses, we can add the exponents 9 and -13.
9 + (-13) = -4
So, the equivalent expression with only positive exponents is 5^(-4).