5^9⋅5^−13
To simplify 5^9•5^−13, we can combine the exponents.
First, let's recall the exponent rule that states: a^m • a^n = a^(m+n)
Using this rule, we can add the exponents 9 and -13: 9 + (-13) = -4.
Therefore, 5^9•5^−13 simplifies to 5^-4.
To simplify the expression 5^9 * 5^(-13), you can use the rule of exponents stating that if you have the same base raised to different exponents, you can multiply the bases and add the exponents.
In this case, the base is 5, and the exponents are 9 and -13. Therefore, the expression can be simplified as follows:
5^9 * 5^(-13) = 5^(9 + (-13))
To add the exponents, we subtract 13 from 9:
5^(9 + (-13)) = 5^(-4)
So, 5^9 * 5^(-13) simplifies to 5^(-4).