Solve (frac{1/a)^{-4}*B^5*A^-2*B}{B^6*A^3}

$$\frac { ( \frac { 1 } { a } ) ^ { - 4 } \times B ^ { 5 } \times A ^ { - 2 } \cdot B } { B ^ { 6 } \times A ^ { 3 } }$$

Evaluate

$$\frac{a^{4}}{A^{5}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{\left(\frac{1}{a}\right)^{-4}B^{6}A^{-2}}{B^{6}A^{3}}$$

To raise \frac{1}{a} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{1^{-4}}{a^{-4}}B^{6}A^{-2}}{B^{6}A^{3}}$$

Express \frac{1^{-4}}{a^{-4}}B^{6} as a single fraction.

$$\frac{\frac{1^{-4}B^{6}}{a^{-4}}A^{-2}}{B^{6}A^{3}}$$

Express \frac{1^{-4}B^{6}}{a^{-4}}A^{-2} as a single fraction.

$$\frac{\frac{1^{-4}B^{6}A^{-2}}{a^{-4}}}{B^{6}A^{3}}$$

Express \frac{\frac{1^{-4}B^{6}A^{-2}}{a^{-4}}}{B^{6}A^{3}} as a single fraction.

$$\frac{1^{-4}B^{6}A^{-2}}{a^{-4}B^{6}A^{3}}$$

Cancel out B^{6} in both numerator and denominator.

$$\frac{1^{-4}A^{-2}}{a^{-4}A^{3}}$$

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

$$\frac{1^{-4}}{a^{-4}A^{5}}$$

Calculate 1 to the power of -4 and get 1.

$$\frac{1}{a^{-4}A^{5}}$$

Differentiate w.r.t. a

$$\frac{4a^{3}}{A^{5}}$$