To simplify this expression, we apply the rule of negative exponents, which states that a negative exponent is equivalent to the reciprocal of the same number raised to the positive exponent.
So, 6^-4 can be rewritten as 1/6^4 and 6^-5 can be rewritten as 1/6^5.
Now, when we divide these two expressions, we get:
(1/6^4) / (1/6^5)
To divide by a fraction, we multiply by the reciprocal of the fraction:
6^-4: 6^-5
To simplify this expression, we apply the rule of negative exponents, which states that a negative exponent is equivalent to the reciprocal of the same number raised to the positive exponent.
So, 6^-4 can be rewritten as 1/6^4 and 6^-5 can be rewritten as 1/6^5.
Now, when we divide these two expressions, we get:
(1/6^4) / (1/6^5)
To divide by a fraction, we multiply by the reciprocal of the fraction:
(1/6^4) * (6^5/1)
Now, we multiply the numerators and denominators:
1 6^5 = 6^5
6^4 1 = 6^4
Therefore, the final simplified expression is:
6^5 / 6^4 = 6^(5-4) = 6^1 = 6