Question

Express the following fraction in simplest form, only using positive exponents.

(
−
4
c
−
1
)
3
12
c
−
8
12c
−8

(−4c
−1
)
3

​

Answer 1

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.