Solve frac{24x^{-5}y^{-3}z^{2}}{36x^{-2}y^{3}z^{-2}}quadtext{79.}x^-5y^-7/x^0y^-4

$$\frac { 24 x ^ { - 5 } y ^ { - 3 } z ^ { 2 } } { 36 x ^ { - 2 } y ^ { 3 } z ^ { - 2 } } \quad \text { 79. } \frac { x ^ { - 5 } y ^ { - 7 } } { x ^ { 0 } y ^ { - 4 } }$$

Evaluate

$$\frac{158z^{4}}{3x^{8}y^{9}}$$

Solution Steps

Cancel out 12 in both numerator and denominator.

$$\frac{2x^{-5}y^{-3}z^{2}}{3x^{-2}z^{-2}y^{3}}\times 79\times \frac{x^{-5}y^{-7}}{x^{0}y^{-4}}$$

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

$$\frac{2x^{-5}y^{-3}z^{4}}{3x^{-2}y^{3}}\times 79\times \frac{x^{-5}y^{-7}}{x^{0}y^{-4}}$$

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

$$\frac{2z^{4}}{3x^{3}y^{6}}\times 79\times \frac{x^{-5}y^{-7}}{x^{0}y^{-4}}$$

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

$$\frac{2z^{4}}{3x^{3}y^{6}}\times 79\times \frac{1}{y^{3}x^{5}}$$

Express \frac{2z^{4}}{3x^{3}y^{6}}\times 79 as a single fraction.

$$\frac{2z^{4}\times 79}{3x^{3}y^{6}}\times \frac{1}{y^{3}x^{5}}$$

Multiply \frac{2z^{4}\times 79}{3x^{3}y^{6}} times \frac{1}{y^{3}x^{5}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2z^{4}\times 79}{3x^{3}y^{6}y^{3}x^{5}}$$

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\frac{2z^{4}\times 79}{3x^{8}y^{6}y^{3}}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{2z^{4}\times 79}{3x^{8}y^{9}}$$

Multiply 2 and 79 to get 158.

$$\frac{158z^{4}}{3x^{8}y^{9}}$$

Differentiate w.r.t. x

$$-\frac{1264z^{4}}{3\left(xy\right)^{9}}$$