Solve (frac{2xy^{2}z^{6}}{3x^5y^6z^4})^-2

$$( \frac { 2 x y ^ { 2 } z ^ { 6 } } { 3 x ^ { 5 } y ^ { 6 } z ^ { 4 } } ) ^ { - 2 }$$

Evaluate

$$\frac{9\left(xy\right)^{8}}{4z^{4}}$$

Solution Steps

Cancel out xy^{2}z^{4} in both numerator and denominator.

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

To raise \frac{2z^{2}}{3x^{4}y^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}z^{-4}}{\left(3x^{4}y^{4}\right)^{-2}}$$

Expand \left(3x^{4}y^{4}\right)^{-2}.

$$\frac{\frac{1}{4}z^{-4}}{3^{-2}\left(x^{4}\right)^{-2}\left(y^{4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{\frac{1}{4}z^{-4}}{3^{-2}x^{-8}\left(y^{4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{\frac{1}{4}z^{-4}}{3^{-2}x^{-8}y^{-8}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{4}z^{-4}}{\frac{1}{9}x^{-8}y^{-8}}$$

Expand

$$\frac{9\left(xy\right)^{8}}{4z^{4}}$$

Solution Steps

Cancel out xy^{2}z^{4} in both numerator and denominator.

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

To raise \frac{2z^{2}}{3x^{4}y^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}z^{-4}}{\left(3x^{4}y^{4}\right)^{-2}}$$

Expand \left(3x^{4}y^{4}\right)^{-2}.

$$\frac{\frac{1}{4}z^{-4}}{3^{-2}\left(x^{4}\right)^{-2}\left(y^{4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{\frac{1}{4}z^{-4}}{3^{-2}x^{-8}\left(y^{4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{\frac{1}{4}z^{-4}}{3^{-2}x^{-8}y^{-8}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{4}z^{-4}}{\frac{1}{9}x^{-8}y^{-8}}$$