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

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

Evaluate

$$10w^{5}x^{31}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 7 to get 28.

$$\frac{6w^{5}x^{3}}{3w^{2}}\times \frac{5x^{28}}{w^{-2}}$$

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

$$2w^{3}x^{3}\times \frac{5x^{28}}{w^{-2}}$$

Express 2\times \frac{5x^{28}}{w^{-2}} as a single fraction.

$$\frac{2\times 5x^{28}}{w^{-2}}w^{3}x^{3}$$

Multiply 2 and 5 to get 10.

$$\frac{10x^{28}}{w^{-2}}w^{3}x^{3}$$

Express \frac{10x^{28}}{w^{-2}}w^{3} as a single fraction.

$$\frac{10x^{28}w^{3}}{w^{-2}}x^{3}$$

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

$$10w^{5}x^{28}x^{3}$$

To multiply powers of the same base, add their exponents. Add 28 and 3 to get 31.

$$10w^{5}x^{31}$$

Differentiate w.r.t. x

$$310w^{5}x^{30}$$