(-4/13)^5 . (26/5)^5

To solve the expression (-4/13)^5 (26/5)^5, we can use the property of exponents that states (a^m) (b^m) = (a * b)^m.

First, we rewrite the expression:

(-4/13)^5 (26/5)^5 = [(-4/13) (26/5)]^5.

Next, we need to calculate the product inside the brackets:

(-4/13) (26/5) = (-4 26) / (13 * 5) = (-104) / 65.

Now we simplify the fraction -104/65. Both -104 and 65 can be divided by 13, which is their greatest common divisor (GCD):

-104 ÷ 13 = -8,
65 ÷ 13 = 5.

Thus, we have:

(-104/65) = (-8/5).

Now we put this back into our exponent expression:

[(-8/5)]^5.

Next, we compute (-8/5)^5. Since we know that (a/b)^n = a^n / b^n, we have:

(-8/5)^5 = (-8)^5 / (5)^5.

Calculating each part separately:

(-8)^5 = -32768 (since raising a negative number to an odd power results in a negative number),
5^5 = 3125.

Putting these together gives:

(-8/5)^5 = -32768 / 3125.

So, the final result is:

(-4/13)^5 * (26/5)^5 = -32768 / 3125.