Solve (frac{4x^{-1}y^{-2}z^3}{2xy^2z^-3})^-2

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

Evaluate

$$\frac{x^{4}y^{8}}{4z^{12}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

$$\left(\frac{2y^{-2}\times \frac{1}{x}z^{6}}{xy^{2}}\right)^{-2}$$

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

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

To raise \frac{2z^{6}}{x^{2}y^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(2z^{6}\right)^{-2}.

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

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$\frac{2^{-2}z^{-12}}{\left(x^{2}y^{4}\right)^{-2}}$$

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

$$\frac{\frac{1}{4}z^{-12}}{\left(x^{2}y^{4}\right)^{-2}}$$

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

$$\frac{\frac{1}{4}z^{-12}}{\left(x^{2}\right)^{-2}\left(y^{4}\right)^{-2}}$$

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

$$\frac{\frac{1}{4}z^{-12}}{x^{-4}\left(y^{4}\right)^{-2}}$$

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

$$\frac{\frac{1}{4}z^{-12}}{x^{-4}y^{-8}}$$

Expand

$$\frac{x^{4}y^{8}}{4z^{12}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

$$\left(\frac{2y^{-2}\times \frac{1}{x}z^{6}}{xy^{2}}\right)^{-2}$$

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

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

To raise \frac{2z^{6}}{x^{2}y^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(2z^{6}\right)^{-2}.

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

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$\frac{2^{-2}z^{-12}}{\left(x^{2}y^{4}\right)^{-2}}$$

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

$$\frac{\frac{1}{4}z^{-12}}{\left(x^{2}y^{4}\right)^{-2}}$$

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

$$\frac{\frac{1}{4}z^{-12}}{\left(x^{2}\right)^{-2}\left(y^{4}\right)^{-2}}$$

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

$$\frac{\frac{1}{4}z^{-12}}{x^{-4}\left(y^{4}\right)^{-2}}$$

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

$$\frac{\frac{1}{4}z^{-12}}{x^{-4}y^{-8}}$$