Answer:
Explanation:
To simplify the fraction (−4c^−1)^3 / (12c^−8), we can apply the rules of exponents.
First, let's simplify the numerator: (-4c^(-1))^3. To raise a power to a power, we multiply the exponents, so we have:
(-4c^(-1))^3 = (-4)^3 * (c^(-1))^3
= -64 * c^(-3)
Now, let's simplify the denominator: 12c^(-8).
Putting the simplified numerator and denominator together, the fraction becomes:
(-64 * c^(-3)) / (12c^(-8))
To simplify further, we can divide the coefficients and subtract the exponents of the variable:
(-64 / 12) * (c^(-3 - (-8)))
= (-64 / 12) * (c^5)
= -16/3 * c^5
So, the fraction (−4c^−1)^3 / (12c^−8) simplifies to (-16/3) * c^5.