Which of the following is an equivalent expression to 5^9×5^-13 with only positive exponents that has been generated by applying the property of integer exponents
The property of integer exponents that we would apply is that multiplying two numbers with the same base but different exponents is equal to adding the exponents.
Let's first simplify the exponent expression by applying the property of exponents:
5^9 × 5^-13 = 5^(9-13) = 5^-4
Now, let's generate an equivalent expression with only positive exponents by applying the property of exponents again:
5^-4 = 1/5^4
Therefore, the equivalent expression with only positive exponents is 1/5^4.
To simplify the expression 5^9 × 5^-13 with only positive exponents using the property of integer exponents, we can combine the exponents.
The property states that when multiplying two numbers with the same base, we add their exponents. Therefore, we can rewrite the expression as:
5^(9 + (-13))
Simplifying the exponent, we get:
5^(-4)
However, we want to find an equivalent expression with only positive exponents. To do this, we can use another property of exponents, which states that any non-zero number raised to a negative exponent is equal to 1 divided by that number raised to the positive exponent. Therefore:
5^(-4) = 1 / 5^4
Hence, an equivalent expression, with only positive exponents, to 5^9 × 5^-13 is 1 / 5^4.