Solve frac{8^{1}m^{5}m^2n^-2}{am^-4n^3}

$$\frac { 8 ^ { 1 } m ^ { 5 } m ^ { 2 } n ^ { - 2 } } { a m ^ { - 4 } n ^ { 3 } }$$

Evaluate

$$\frac{8m^{11}}{an^{5}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{8^{1}m^{7}n^{-2}}{am^{-4}n^{3}}$$

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

$$\frac{8^{1}n^{-2}m^{11}}{an^{3}}$$

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

$$\frac{8^{1}m^{11}}{an^{5}}$$

Calculate 8 to the power of 1 and get 8.

$$\frac{8m^{11}}{an^{5}}$$

Differentiate w.r.t. a

$$-\frac{8m^{11}}{a^{2}n^{5}}$$