Solve frac{10q^{5}w^{7}}{2w^3}*4(q^6)^2/w^-5

$$\frac { 10 q ^ { 5 } w ^ { 7 } } { 2 w ^ { 3 } } \cdot \frac { 4 ( q ^ { 6 } ) ^ { 2 } } { w ^ { - 5 } }$$

Evaluate

$$20w^{9}q^{17}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{10q^{5}w^{7}}{2w^{3}}\times \frac{4q^{12}}{w^{-5}}$$

Cancel out 2w^{3} in both numerator and denominator.

$$5w^{4}q^{5}\times \frac{4q^{12}}{w^{-5}}$$

Express 5\times \frac{4q^{12}}{w^{-5}} as a single fraction.

$$\frac{5\times 4q^{12}}{w^{-5}}w^{4}q^{5}$$

Multiply 5 and 4 to get 20.

$$\frac{20q^{12}}{w^{-5}}w^{4}q^{5}$$

Express \frac{20q^{12}}{w^{-5}}w^{4} as a single fraction.

$$\frac{20q^{12}w^{4}}{w^{-5}}q^{5}$$

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

$$20w^{9}q^{12}q^{5}$$

To multiply powers of the same base, add their exponents. Add 12 and 5 to get 17.

$$20w^{9}q^{17}$$

Differentiate w.r.t. q

$$340w^{9}q^{16}$$