Final answer:
To simplify the expression (-10a⁷b⁴c⁵/(25a³b⁴c³)³), the denominator is first cubed, after which the numerator and denominator are divided, subtracting the corresponding exponents. The simplified expression is -0.00064/(a^2b^8c^4).
Step-by-step explanation:
The question requires simplifying the given integer exponents: (-10a⁷b⁴c⁵/(25a³b⁴c³)³). To do this, we apply the rules of cubing of exponentials and division of exponentials.
First, let's expand and cube the denominator as indicated:
(25a³b⁴c³)³ = 25³ x (a³)³ x (b⁴)³ x (c³)³
25³ = 15625
(a³)³ = a⁹
(b⁴)³ = b¹²
(c³)³ = c⁹
So the denominator becomes 15625a⁹b¹²c⁹.
Now we divide the terms:
-10a⁷b⁴c⁵ / 15625a⁹b¹²c⁹
The coefficient division yields (-10/15625), which reduces to -0.00064. For the variable terms, we subtract the exponents due to division (remember that subtracting a larger exponent from a smaller one will result in a negative exponent, indicating an inverse):
a⁷ / a⁹ = a^(7-9) = a^-2
b⁴ / b¹² = b^(4-12) = b^-8
c⁵ / c⁹ = c^(5-9) = c^-4
Combining these, we get:
-0.00064a^-2b^-8c^-4
In positive exponent form (reciprocals for negative exponents) it is:
-0.00064/(a^2b^8c^4)