Question

what is an equivalent expression to 5^9* 5^-13 with only positive exponents that has been generated by applying the properties of integer exponents

Answer 1

By applying the properties of integer exponents, we can simplify the expression 5^9 * 5^-13 to an equivalent expression with positive exponents.

The property we will use is: a^m * a^n = a^(m + n)

So, for our expression: 5^9 * 5^-13

We can rewrite it as: 5^(9 + (-13))

Now, simplify the exponents: 5^(-4)

To make the exponent positive, we can use the property: a^(-n) = 1 / a^n

So, 5^(-4) can be written as: 1 / 5^4

Therefore, the equivalent expression to 5^9 * 5^-13 with only positive exponents is 1 / 5^4.