Solve (6*t^3/t^2*y^5)^-1

$$( \frac { 6 \cdot t ^ { 3 } } { t ^ { 2 } \cdot y ^ { 5 } } ) ^ { - 1 }$$

Evaluate

$$\frac{y^{5}}{6t}$$

Solution Steps

Cancel out t^{2} in both numerator and denominator.

$$\left(\frac{6t}{y^{5}}\right)^{-1}$$

To raise \frac{6t}{y^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(6t\right)^{-1}}{\left(y^{5}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -1 to get -5.

$$\frac{\left(6t\right)^{-1}}{y^{-5}}$$

Expand \left(6t\right)^{-1}.

$$\frac{6^{-1}t^{-1}}{y^{-5}}$$

Calculate 6 to the power of -1 and get \frac{1}{6}.

$$\frac{\frac{1}{6}t^{-1}}{y^{-5}}$$

Differentiate w.r.t. y

$$\frac{5y^{4}}{6t}$$