Solve (16/m^8)^frac{1{4}}*m^-3

$$( \frac { 16 } { m ^ { 8 } } ) ^ { \frac { 1 } { 4 } } \times m ^ { - 3 }$$

Evaluate

$$\frac{2}{m^{5}}$$

Solution Steps

To raise \frac{16}{m^{8}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{16^{\frac{1}{4}}}{\left(m^{8}\right)^{\frac{1}{4}}}m^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 8 and \frac{1}{4} to get 2.

$$\frac{16^{\frac{1}{4}}}{m^{2}}m^{-3}$$

Calculate 16 to the power of \frac{1}{4} and get 2.

$$\frac{2}{m^{2}}m^{-3}$$

Express \frac{2}{m^{2}}m^{-3} as a single fraction.

$$\frac{2m^{-3}}{m^{2}}$$

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

$$\frac{2}{m^{5}}$$

Differentiate w.r.t. m

$$-\frac{10}{m^{6}}$$