Solve frac{6a^{3}b^{-7}c^{0}*18a^{-5}b^3}{-9a^-5b^-1c^4}

$$\frac { 6 a ^ { 3 } b ^ { - 7 } c ^ { 0 } \times 18 a ^ { - 5 } b ^ { 3 } } { - 9 a ^ { - 5 } b ^ { - 1 } c ^ { 4 } }$$

Evaluate

$$-\frac{12\times \left(\frac{a}{b}\right)^{3}}{c^{4}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -5 to get -2.

$$\frac{6a^{-2}b^{-7}c^{0}\times 18b^{3}}{-9a^{-5}b^{-1}c^{4}}$$

To multiply powers of the same base, add their exponents. Add -7 and 3 to get -4.

$$\frac{6a^{-2}b^{-4}c^{0}\times 18}{-9a^{-5}b^{-1}c^{4}}$$

Cancel out 3\times 3 in both numerator and denominator.

$$\frac{2\times 6b^{-4}a^{-2}c^{0}}{-a^{-5}\times \frac{1}{b}c^{4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{2\times 6b^{-4}c^{0}a^{3}}{-\frac{1}{b}c^{4}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{2\times 6a^{3}}{-b^{3}c^{4}}$$

Multiply 2 and 6 to get 12.

$$\frac{12a^{3}}{-b^{3}c^{4}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{-12a^{3}}{b^{3}c^{4}}$$

Differentiate w.r.t. b

$$\frac{36a^{3}}{\left(bc\right)^{4}}$$