Solve frac{(x^{-3}y^{4})^{2}z^3}{x^-7y^4z^0}

$$\frac { ( x ^ { - 3 } y ^ { 4 } ) ^ { 2 } z ^ { 3 } } { x ^ { - 7 } y ^ { 4 } z ^ { 0 } }$$

Evaluate

$$xz^{3}y^{4}$$

Solution Steps

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

$$\frac{\left(x^{-3}y^{4}\right)^{2}z^{3}}{x^{-7}y^{4}}$$

Expand \left(x^{-3}y^{4}\right)^{2}.

$$\frac{\left(x^{-3}\right)^{2}\left(y^{4}\right)^{2}z^{3}}{x^{-7}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 2 to get -6.

$$\frac{x^{-6}\left(y^{4}\right)^{2}z^{3}}{x^{-7}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{x^{-6}y^{8}z^{3}}{x^{-7}y^{4}}$$

Cancel out y^{4} in both numerator and denominator.

$$\frac{x^{-6}z^{3}y^{4}}{x^{-7}}$$

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

$$x^{1}z^{3}y^{4}$$

Calculate x to the power of 1 and get x.

$$xz^{3}y^{4}$$

Differentiate w.r.t. x

$$z^{3}y^{4}$$