Solve frac{(2x^{3}y^2)^-2}{z^2}:x^2z/y=

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

Evaluate

$$\frac{1}{4x^{8}\left(yz\right)^{3}}$$

Solution Steps

Divide \frac{\left(2x^{3}y^{2}\right)^{-2}}{z^{2}} by \frac{x^{2}z}{y} by multiplying \frac{\left(2x^{3}y^{2}\right)^{-2}}{z^{2}} by the reciprocal of \frac{x^{2}z}{y}.

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

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

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

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

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

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

$$\frac{2^{-2}x^{-6}y^{-4}y}{z^{2}x^{2}z}$$

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

$$\frac{\frac{1}{4}x^{-6}y^{-4}y}{z^{2}x^{2}z}$$

To multiply powers of the same base, add their exponents. Add -4 and 1 to get -3.

$$\frac{\frac{1}{4}x^{-6}y^{-3}}{z^{2}x^{2}z}$$

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

$$\frac{\frac{1}{4}x^{-6}y^{-3}}{z^{3}x^{2}}$$

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

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

Expand

$$\frac{1}{4x^{8}\left(yz\right)^{3}}$$

Solution Steps

Divide \frac{\left(2x^{3}y^{2}\right)^{-2}}{z^{2}} by \frac{x^{2}z}{y} by multiplying \frac{\left(2x^{3}y^{2}\right)^{-2}}{z^{2}} by the reciprocal of \frac{x^{2}z}{y}.

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

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

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

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

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

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

$$\frac{2^{-2}x^{-6}y^{-4}y}{z^{2}x^{2}z}$$

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

$$\frac{\frac{1}{4}x^{-6}y^{-4}y}{z^{2}x^{2}z}$$

To multiply powers of the same base, add their exponents. Add -4 and 1 to get -3.

$$\frac{\frac{1}{4}x^{-6}y^{-3}}{z^{2}x^{2}z}$$

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

$$\frac{\frac{1}{4}x^{-6}y^{-3}}{z^{3}x^{2}}$$

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

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