Solve frac{(7x^{10}y^{-15}z^{5})^{0}}{[12x^{2}(y^{8})^-3(z^3)^2]^1}

$$\frac { ( 7 x ^ { 10 } y ^ { - 15 } z ^ { 5 } ) ^ { 0 } } { [ 12 x ^ { 2 } ( y ^ { 8 } ) ^ { - 3 } ( z ^ { 3 } ) ^ { 2 } ] ^ { 1 } }$$

Evaluate

$$\frac{y^{24}}{12x^{2}z^{6}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 8 and -3 to get -24.

$$\frac{\left(7x^{10}y^{-15}z^{5}\right)^{0}}{\left(12x^{2}y^{-24}\left(z^{3}\right)^{2}\right)^{1}}$$

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

$$\frac{\left(7x^{10}y^{-15}z^{5}\right)^{0}}{\left(12x^{2}y^{-24}z^{6}\right)^{1}}$$

Calculate 7x^{10}y^{-15}z^{5} to the power of 0 and get 1.

$$\frac{1}{\left(12x^{2}y^{-24}z^{6}\right)^{1}}$$

Calculate 12x^{2}y^{-24}z^{6} to the power of 1 and get 12x^{2}y^{-24}z^{6}.

$$\frac{1}{12x^{2}y^{-24}z^{6}}$$

Differentiate w.r.t. x

$$-\frac{y^{24}}{6x^{3}z^{6}}$$