Solve frac{(frac{y^{2}}{z^{3}})^{-2}*(frac{z^{2}}{y^{3}})^2}{(y^-3*z^3)^3}

$$\frac { ( \frac { y ^ { 2 } } { z ^ { 3 } } ) ^ { - 2 } \cdot ( \frac { z ^ { 2 } } { y ^ { 3 } } ) ^ { 2 } } { ( y ^ { - 3 } \cdot z ^ { 3 } ) ^ { 3 } }$$

Evaluate

$$\frac{z}{y}$$

Solution Steps

To raise \frac{y^{2}}{z^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{\left(y^{2}\right)^{-2}}{\left(z^{3}\right)^{-2}}\times \left(\frac{z^{2}}{y^{3}}\right)^{2}}{\left(y^{-3}z^{3}\right)^{3}}$$

To raise \frac{z^{2}}{y^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{\left(y^{2}\right)^{-2}}{\left(z^{3}\right)^{-2}}\times \frac{\left(z^{2}\right)^{2}}{\left(y^{3}\right)^{2}}}{\left(y^{-3}z^{3}\right)^{3}}$$

Multiply \frac{\left(y^{2}\right)^{-2}}{\left(z^{3}\right)^{-2}} times \frac{\left(z^{2}\right)^{2}}{\left(y^{3}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Expand \left(y^{-3}z^{3}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$\frac{\frac{\left(y^{2}\right)^{-2}\left(z^{2}\right)^{2}}{\left(z^{3}\right)^{-2}\left(y^{3}\right)^{2}}}{y^{-9}\left(z^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\frac{\left(y^{2}\right)^{-2}\left(z^{2}\right)^{2}}{\left(z^{3}\right)^{-2}\left(y^{3}\right)^{2}}}{y^{-9}z^{9}}$$

Express \frac{\frac{\left(y^{2}\right)^{-2}\left(z^{2}\right)^{2}}{\left(z^{3}\right)^{-2}\left(y^{3}\right)^{2}}}{y^{-9}z^{9}} as a single fraction.

$$\frac{\left(y^{2}\right)^{-2}\left(z^{2}\right)^{2}}{\left(z^{3}\right)^{-2}\left(y^{3}\right)^{2}y^{-9}z^{9}}$$

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

$$\frac{y^{-4}\left(z^{2}\right)^{2}}{\left(z^{3}\right)^{-2}\left(y^{3}\right)^{2}y^{-9}z^{9}}$$

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

$$\frac{y^{-4}z^{4}}{\left(z^{3}\right)^{-2}\left(y^{3}\right)^{2}y^{-9}z^{9}}$$

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

$$\frac{y^{-4}z^{4}}{z^{-6}\left(y^{3}\right)^{2}y^{-9}z^{9}}$$

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

$$\frac{y^{-4}z^{4}}{z^{-6}y^{6}y^{-9}z^{9}}$$

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

$$\frac{y^{-4}z^{4}}{z^{3}y^{6}y^{-9}}$$

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

$$\frac{y^{-4}z^{4}}{z^{3}y^{-3}}$$

Cancel out z^{3} in both numerator and denominator.

$$\frac{y^{-4}z}{y^{-3}}$$

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

$$\frac{z}{y^{1}}$$

Calculate y to the power of 1 and get y.

$$\frac{z}{y}$$

Expand

$$\frac{z}{y}$$

Solution Steps

To raise \frac{y^{2}}{z^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{\left(y^{2}\right)^{-2}}{\left(z^{3}\right)^{-2}}\times \left(\frac{z^{2}}{y^{3}}\right)^{2}}{\left(y^{-3}z^{3}\right)^{3}}$$

To raise \frac{z^{2}}{y^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{\left(y^{2}\right)^{-2}}{\left(z^{3}\right)^{-2}}\times \frac{\left(z^{2}\right)^{2}}{\left(y^{3}\right)^{2}}}{\left(y^{-3}z^{3}\right)^{3}}$$

Multiply \frac{\left(y^{2}\right)^{-2}}{\left(z^{3}\right)^{-2}} times \frac{\left(z^{2}\right)^{2}}{\left(y^{3}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Expand \left(y^{-3}z^{3}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$\frac{\frac{\left(y^{2}\right)^{-2}\left(z^{2}\right)^{2}}{\left(z^{3}\right)^{-2}\left(y^{3}\right)^{2}}}{y^{-9}\left(z^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\frac{\left(y^{2}\right)^{-2}\left(z^{2}\right)^{2}}{\left(z^{3}\right)^{-2}\left(y^{3}\right)^{2}}}{y^{-9}z^{9}}$$

Express \frac{\frac{\left(y^{2}\right)^{-2}\left(z^{2}\right)^{2}}{\left(z^{3}\right)^{-2}\left(y^{3}\right)^{2}}}{y^{-9}z^{9}} as a single fraction.

$$\frac{\left(y^{2}\right)^{-2}\left(z^{2}\right)^{2}}{\left(z^{3}\right)^{-2}\left(y^{3}\right)^{2}y^{-9}z^{9}}$$

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

$$\frac{y^{-4}\left(z^{2}\right)^{2}}{\left(z^{3}\right)^{-2}\left(y^{3}\right)^{2}y^{-9}z^{9}}$$

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

$$\frac{y^{-4}z^{4}}{\left(z^{3}\right)^{-2}\left(y^{3}\right)^{2}y^{-9}z^{9}}$$

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

$$\frac{y^{-4}z^{4}}{z^{-6}\left(y^{3}\right)^{2}y^{-9}z^{9}}$$

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

$$\frac{y^{-4}z^{4}}{z^{-6}y^{6}y^{-9}z^{9}}$$

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

$$\frac{y^{-4}z^{4}}{z^{3}y^{6}y^{-9}}$$

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

$$\frac{y^{-4}z^{4}}{z^{3}y^{-3}}$$

Cancel out z^{3} in both numerator and denominator.

$$\frac{y^{-4}z}{y^{-3}}$$

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

$$\frac{z}{y^{1}}$$

Calculate y to the power of 1 and get y.

$$\frac{z}{y}$$