Solve frac{(2x^{6})^3y^7}{x^-2y^0}

$$\frac { ( 2 x ^ { 6 } ) ^ { 3 } y ^ { 7 } } { x ^ { - 2 } y ^ { 0 } }$$

Evaluate

$$8y^{7}x^{20}$$

Solution Steps

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

$$\frac{y^{7}\times \left(2x^{6}\right)^{3}}{x^{-2}}$$

Expand \left(2x^{6}\right)^{3}.

$$\frac{y^{7}\times 2^{3}\left(x^{6}\right)^{3}}{x^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{y^{7}\times 2^{3}x^{18}}{x^{-2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{y^{7}\times 8x^{18}}{x^{-2}}$$

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

$$8y^{7}x^{20}$$

Differentiate w.r.t. x

$$160y^{7}x^{19}$$