Solve (2k^-4/k^3)^-1*3/k

$$( \frac { 2 k ^ { - 4 } } { k ^ { 3 } } ) ^ { - 1 } \cdot \frac { 3 } { k }$$

Evaluate

$$\frac{3k^{6}}{2}$$

Solution Steps

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

$$\left(\frac{2}{k^{7}}\right)^{-1}\times \frac{3}{k}$$

To raise \frac{2}{k^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{2^{-1}}{\left(k^{7}\right)^{-1}}\times \frac{3}{k}$$

Multiply \frac{2^{-1}}{\left(k^{7}\right)^{-1}} times \frac{3}{k} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2^{-1}\times 3}{\left(k^{7}\right)^{-1}k}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -1 to get -7.

$$\frac{2^{-1}\times 3}{k^{-7}k}$$

To multiply powers of the same base, add their exponents. Add -7 and 1 to get -6.

$$\frac{2^{-1}\times 3}{k^{-6}}$$

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

$$\frac{\frac{1}{2}\times 3}{k^{-6}}$$

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$\frac{\frac{3}{2}}{k^{-6}}$$

Express \frac{\frac{3}{2}}{k^{-6}} as a single fraction.

$$\frac{3}{2k^{-6}}$$

Differentiate w.r.t. k

$$9k^{5}$$