Solve frac{6^{-2}a^{-1}b^{3}c^-5}{2^-3ab^-1c^-2}

$$\frac { 6 ^ { - 2 } a ^ { - 1 } b ^ { 3 } c ^ { - 5 } } { 2 ^ { - 3 } a b ^ { - 1 } c ^ { - 2 } }$$

Evaluate

$$\frac{2b^{4}}{9a^{2}c^{3}}$$

Solution Steps

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

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

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

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

Calculate 6 to the power of -2 and get \frac{1}{36}.

$$\frac{\frac{1}{36}b^{4}}{2^{-3}a^{2}c^{3}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{1}{36}b^{4}}{\frac{1}{8}a^{2}c^{3}}$$

Differentiate w.r.t. c

$$-\frac{2\times \left(\frac{b}{c}\right)^{4}}{3a^{2}}$$