Solve frac{6^{-1}a^-3b^4}{5^-2ab^5}

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

Evaluate

$$\frac{25}{6ba^{4}}$$

Solution Steps

Cancel out b^{4} in both numerator and denominator.

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

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

$$\frac{\frac{1}{6}}{5^{-2}ba^{4}}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{\frac{1}{6}}{\frac{1}{25}ba^{4}}$$

Express \frac{\frac{1}{6}}{\frac{1}{25}ba^{4}} as a single fraction.

$$\frac{1}{6\times \frac{1}{25}ba^{4}}$$

Multiply 6 and \frac{1}{25} to get \frac{6}{25}.

$$\frac{1}{\frac{6}{25}ba^{4}}$$

Differentiate w.r.t. b

$$-\frac{25}{6b^{2}a^{4}}$$