Question

Simplify. \(-18 c^{3} \div \frac{-27 c}{-4}\)

Short answer

The simplified form is \(121.5 c^{4}\)

Step-by-step solution

Address the Negative Signs

First, let's address the negative signs. In arithmetic, whenever one divides by a negative number, it can be rewritten as a multiplication with the same number but with a reversed sign: thus \(-18 c^{3} \div \frac{-27 c}{-4} = -18 c^{3} \times \frac{-27 c}{4} = -18 c^{3} \times -\frac{27 c}{4} = 18 c^{3} \times \frac{27 c}{4}\)

Multiply Monomials with the Fraction

Respect the multiplication order and multiply the monomial with the numerator of the fraction: \(18 c^{3} \times 27 c = 486 c^{4}\)

Handle the Denominator

Remember that when a number is being divided by another number, we can rewrite the division as multiplication by the reciprocal of the divisor. Thus, the original problem of \(18 c^{3} \times 27 c \div 4\) can be rewritten as \(486 c^{4} \times \frac{1}{4}\)

Final Calculation

Finally, multiply the number obtained in the previous step by \(\frac{1}{4}\): \(486 c^{4} \times \frac{1}{4} = 121.5 c^{4}\)