Solve [(frac{122x^{9}y^{21}}{69x^-23y^56z^-92})(2z^61)]

$$[ ( \frac { 122 x ^ { 9 } y ^ { 21 } } { 69 x ^ { - 23 } y ^ { 56 } z ^ { - 92 } } ) ( 2 z ^ { 61 } ) ]$$

Evaluate

$$\frac{244x^{32}z^{153}}{69y^{35}}$$

Solution Steps

Cancel out y^{21} in both numerator and denominator.

$$\frac{122x^{9}}{69z^{-92}x^{-23}y^{35}}\times 2z^{61}$$

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

$$\frac{122x^{32}}{69z^{-92}y^{35}}\times 2z^{61}$$

Express \frac{122x^{32}}{69z^{-92}y^{35}}\times 2 as a single fraction.

$$\frac{122x^{32}\times 2}{69z^{-92}y^{35}}z^{61}$$

Express \frac{122x^{32}\times 2}{69z^{-92}y^{35}}z^{61} as a single fraction.

$$\frac{122x^{32}\times 2z^{61}}{69z^{-92}y^{35}}$$

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

$$\frac{2\times 122x^{32}z^{153}}{69y^{35}}$$

Multiply 2 and 122 to get 244.

$$\frac{244x^{32}z^{153}}{69y^{35}}$$

Differentiate w.r.t. x

$$\frac{7808x^{31}z^{153}}{69y^{35}}$$