simplify the expression using the properties of rational exponents
13 to a power of(-5/4)
I THINK, SO I'M NO SURE...
13 to a power of (-5/4)
means....
13 to a power of (-5 divided by 4)
To simplify the expression 13 raised to the power of -5/4 using the properties of rational exponents, we can make use of the following property:
a^(m/n) = (n√a)^m
According to this property, we can rewrite 13^(-5/4) as (4√13)^-5.
Now, let's simplify further by applying another property:
(a^m)^n = a^(m*n)
In this case, we have (4√13)^-5, and we can rewrite it as 1 / (4√13)^5.
Now let's simplify the expression under the square root:
√13 can be written as 13^(1/2).
Therefore, the expression becomes 1 / (4(13)^(1/2))^5.
Now let's simplify the denominator:
(13)^(1/2) raised to the power of 5 can be expressed as (13)^(1/2 * 5), which is equal to (13)^(5/2).
So, the simplified expression is 1 / (4(13)^(5/2)).