Solve (2xy/6x^2)^2(y^2/xz)^-3

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

Evaluate

$$\frac{xz^{3}}{9y^{4}}$$

Solution Steps

Cancel out 2x in both numerator and denominator.

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

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

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

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

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

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

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

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

$$\frac{y^{2}y^{-6}}{\left(3x\right)^{2}\left(xz\right)^{-3}}$$

To multiply powers of the same base, add their exponents. Add 2 and -6 to get -4.

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

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

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

Calculate 3 to the power of 2 and get 9.

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

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

$$\frac{y^{-4}}{9x^{2}x^{-3}z^{-3}}$$

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

$$\frac{y^{-4}}{9x^{-1}z^{-3}}$$

Expand

$$\frac{xz^{3}}{9y^{4}}$$

Solution Steps

Cancel out 2x in both numerator and denominator.

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

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

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

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

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

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

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

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

$$\frac{y^{2}y^{-6}}{\left(3x\right)^{2}\left(xz\right)^{-3}}$$

To multiply powers of the same base, add their exponents. Add 2 and -6 to get -4.

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

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

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

Calculate 3 to the power of 2 and get 9.

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

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

$$\frac{y^{-4}}{9x^{2}x^{-3}z^{-3}}$$

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

$$\frac{y^{-4}}{9x^{-1}z^{-3}}$$