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) 1/625 44455 1/(5 ^ 4); (5 ^ 3)/(5 ^ - 12); 5 ^ 4
The equivalent expression to 5 ^ 9 * 5 ^ - 13 with only positive exponents is 5 ^ (9 - 13) = 5 ^ -4
So, the correct option is: 1/(5 ^ 4)
To simplify the given expression, 5 ^ 9 * 5 ^ - 13, we can use the properties of integer exponents.
The property states that when you multiply two numbers with the same base, you add their exponents. Therefore, applying this property, we can rewrite the expression as:
5 ^ (9 + (-13))
Next, we simplify the exponent by adding the numbers:
5 ^ (-4)
Since we want an expression with only positive exponents, we can take the reciprocal of the expression with a negative exponent. Applying this, we can rewrite the expression as:
1 / (5 ^ 4)
Hence, the equivalent expression with only positive exponents generated by applying the properties of integer exponents is 1/(5 ^ 4).
To find an equivalent expression with only positive exponents, we can use the properties of integer exponents:
1. Rule: When a base is raised to two exponents that are added, we can multiply the base and add the exponents.
2. Rule: When a base is raised to two exponents that are subtracted, we can divide the base and subtract the exponents.
Given the expression: 5^9 * 5^(-13)
1. Applying the first rule, we can multiply the bases and add the exponents since they have the same base:
5^(9 + (-13))
2. Adding the exponents, we get:
5^(-4)
Thus, the equivalent expression with only positive exponents is 1/(5^4). So, the correct answer is:
1/(5^4)