simplify
5^0 1 (5^2)^4
---- * ---- / -----
5^-6 5^-11 (5^10)^2
To simplify this expression, we need to use the rules of exponents and simplify each term separately.
Let's start by simplifying the numerator:
5^0 = 1
Next, let's simplify the first term in the denominator:
5^-6 = 1/5^6
For the second term in the denominator:
5^-11 = 1/5^11
Finally, let's simplify the exponent in the last term:
(5^10)^2 = 5^20
Now, we can substitute these simplified terms back into the expression:
(1 * 1) / (1/5^6 * 1/5^11 * 5^20)
To multiply fractions, we can multiply the numerators together and the denominators together:
1 / (1 * 1 * 5^6 * 5^11 * 5^20)
We can simplify this by adding the exponents of 5:
1 / (5^6+11+20)
Now, simplify the exponent in the denominator:
1 / 5^37
So, the simplified expression is 1 / 5^37.