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 intiger exponents?
1/625
5^4
1/5^4
5^9/5^-13
To find an equivalent expression with positive exponents, we can use the property that says when dividing with the same base, we subtract the exponents. In this case, we have the expression 5^9 • 5^-13. This can be simplified as 5^(9 + (-13)).
The sum of exponents 9 and -13 is -4.
Therefore, an equivalent expression with positive exponents would be 5^-4, which is the same as 1/5^4.
So the correct answer is 1/5^4.
To find an equivalent expression with only positive exponents, we can simplify the exponents using the properties of integer exponents.
First, let’s simplify the exponents in the expression 5^9 * 5^-13:
5^9 * 5^-13
Now, apply the property of exponents that states: a^m * a^n = a^(m+n)
This means that we can combine the exponents by adding them together:
5^(9 + -13)
Now, simplify the expression:
5^(-4)
Since the exponent is negative, we can rewrite it as the reciprocal of the base with the positive exponent:
1/5^4
Therefore, the equivalent expression with only positive exponents is 1/5^4.
To find an equivalent expression with positive exponents, we can apply the properties of integer exponents. The property we'll use here is:
a^m / a^n = a^(m - n)
Applying this property to the expression 5^9 • 5^(-13), we can rewrite it as:
5^(9 - 13)
Simplifying further, we get:
5^(-4)
Therefore, the correct equivalent expression with positive exponents is 1/5^4.