Solve frac{-4(y^{-4}z^{2})^{5}(4)(yz^{5})^{-3}}{-12(y^{5}z)^4(-3)(y^5z^5)^-1}

$$\frac { - 4 ( y ^ { - 4 } z ^ { 2 } ) ^ { 5 } ( 4 ) ( y z ^ { 5 } ) ^ { - 3 } } { - 12 ( y ^ { 5 } z ) ^ { 4 } ( - 3 ) ( y ^ { 5 } z ^ { 5 } ) ^ { - 1 } }$$

Evaluate

$$-\frac{4}{9z^{4}y^{38}}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\frac{-4\left(y^{-4}z^{2}\right)^{5}\left(yz^{5}\right)^{-3}}{-3\left(-3\right)\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

Expand \left(y^{-4}z^{2}\right)^{5}.

$$\frac{-4\left(y^{-4}\right)^{5}\left(z^{2}\right)^{5}\left(yz^{5}\right)^{-3}}{-3\left(-3\right)\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and 5 to get -20.

$$\frac{-4y^{-20}\left(z^{2}\right)^{5}\left(yz^{5}\right)^{-3}}{-3\left(-3\right)\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{-4y^{-20}z^{10}\left(yz^{5}\right)^{-3}}{-3\left(-3\right)\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

Expand \left(yz^{5}\right)^{-3}.

$$\frac{-4y^{-20}z^{10}y^{-3}\left(z^{5}\right)^{-3}}{-3\left(-3\right)\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -3 to get -15.

$$\frac{-4y^{-20}z^{10}y^{-3}z^{-15}}{-3\left(-3\right)\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add -20 and -3 to get -23.

$$\frac{-4y^{-23}z^{10}z^{-15}}{-3\left(-3\right)\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add 10 and -15 to get -5.

$$\frac{-4y^{-23}z^{-5}}{-3\left(-3\right)\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

Multiply -3 and -3 to get 9.

$$\frac{-4y^{-23}z^{-5}}{9\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

Expand \left(zy^{5}\right)^{4}.

$$\frac{-4y^{-23}z^{-5}}{9\times \frac{1}{y^{5}z^{5}}z^{4}\left(y^{5}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{-4y^{-23}z^{-5}}{9\times \frac{1}{y^{5}z^{5}}z^{4}y^{20}}$$

Express 9\times \frac{1}{y^{5}z^{5}} as a single fraction.

$$\frac{-4y^{-23}z^{-5}}{\frac{9}{y^{5}z^{5}}z^{4}y^{20}}$$

Express \frac{9}{y^{5}z^{5}}z^{4} as a single fraction.

$$\frac{-4y^{-23}z^{-5}}{\frac{9z^{4}}{y^{5}z^{5}}y^{20}}$$

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

$$\frac{-4y^{-23}z^{-5}}{\frac{9}{zy^{5}}y^{20}}$$

Express \frac{9}{zy^{5}}y^{20} as a single fraction.

$$\frac{-4y^{-23}z^{-5}}{\frac{9y^{20}}{zy^{5}}}$$

Cancel out y^{5} in both numerator and denominator.

$$\frac{-4y^{-23}z^{-5}}{\frac{9y^{15}}{z}}$$

Divide -4y^{-23}z^{-5} by \frac{9y^{15}}{z} by multiplying -4y^{-23}z^{-5} by the reciprocal of \frac{9y^{15}}{z}.

$$\frac{-4y^{-23}z^{-5}z}{9y^{15}}$$

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

$$\frac{-4z^{-5}z}{9y^{38}}$$

To multiply powers of the same base, add their exponents. Add -5 and 1 to get -4.

$$\frac{-4z^{-4}}{9y^{38}}$$

Expand

$$-\frac{4}{9z^{4}y^{38}}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\frac{-4\left(y^{-4}z^{2}\right)^{5}\left(yz^{5}\right)^{-3}}{-3\left(-3\right)\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

Expand \left(y^{-4}z^{2}\right)^{5}.

$$\frac{-4\left(y^{-4}\right)^{5}\left(z^{2}\right)^{5}\left(yz^{5}\right)^{-3}}{-3\left(-3\right)\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and 5 to get -20.

$$\frac{-4y^{-20}\left(z^{2}\right)^{5}\left(yz^{5}\right)^{-3}}{-3\left(-3\right)\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{-4y^{-20}z^{10}\left(yz^{5}\right)^{-3}}{-3\left(-3\right)\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

Expand \left(yz^{5}\right)^{-3}.

$$\frac{-4y^{-20}z^{10}y^{-3}\left(z^{5}\right)^{-3}}{-3\left(-3\right)\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -3 to get -15.

$$\frac{-4y^{-20}z^{10}y^{-3}z^{-15}}{-3\left(-3\right)\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add -20 and -3 to get -23.

$$\frac{-4y^{-23}z^{10}z^{-15}}{-3\left(-3\right)\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

To multiply powers of the same base, add their exponents. Add 10 and -15 to get -5.

$$\frac{-4y^{-23}z^{-5}}{-3\left(-3\right)\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

Multiply -3 and -3 to get 9.

$$\frac{-4y^{-23}z^{-5}}{9\times \frac{1}{y^{5}z^{5}}\left(zy^{5}\right)^{4}}$$

Expand \left(zy^{5}\right)^{4}.

$$\frac{-4y^{-23}z^{-5}}{9\times \frac{1}{y^{5}z^{5}}z^{4}\left(y^{5}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{-4y^{-23}z^{-5}}{9\times \frac{1}{y^{5}z^{5}}z^{4}y^{20}}$$

Express 9\times \frac{1}{y^{5}z^{5}} as a single fraction.

$$\frac{-4y^{-23}z^{-5}}{\frac{9}{y^{5}z^{5}}z^{4}y^{20}}$$

Express \frac{9}{y^{5}z^{5}}z^{4} as a single fraction.

$$\frac{-4y^{-23}z^{-5}}{\frac{9z^{4}}{y^{5}z^{5}}y^{20}}$$

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

$$\frac{-4y^{-23}z^{-5}}{\frac{9}{zy^{5}}y^{20}}$$

Express \frac{9}{zy^{5}}y^{20} as a single fraction.

$$\frac{-4y^{-23}z^{-5}}{\frac{9y^{20}}{zy^{5}}}$$

Cancel out y^{5} in both numerator and denominator.

$$\frac{-4y^{-23}z^{-5}}{\frac{9y^{15}}{z}}$$

Divide -4y^{-23}z^{-5} by \frac{9y^{15}}{z} by multiplying -4y^{-23}z^{-5} by the reciprocal of \frac{9y^{15}}{z}.

$$\frac{-4y^{-23}z^{-5}z}{9y^{15}}$$

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

$$\frac{-4z^{-5}z}{9y^{38}}$$

To multiply powers of the same base, add their exponents. Add -5 and 1 to get -4.

$$\frac{-4z^{-4}}{9y^{38}}$$