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

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

Evaluate

$$\frac{y^{8}x^{10}}{z^{4}}$$

Solution Steps

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

$$\left(\frac{z^{-3}y^{4}x^{5}}{\frac{1}{z}}\right)^{2}$$

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

$$\left(\frac{y^{4}x^{5}}{z^{2}}\right)^{2}$$

To raise \frac{y^{4}x^{5}}{z^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(y^{4}x^{5}\right)^{2}}{\left(z^{2}\right)^{2}}$$

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

$$\frac{\left(y^{4}x^{5}\right)^{2}}{z^{4}}$$

Expand \left(y^{4}x^{5}\right)^{2}.

$$\frac{\left(y^{4}\right)^{2}\left(x^{5}\right)^{2}}{z^{4}}$$

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

$$\frac{y^{8}\left(x^{5}\right)^{2}}{z^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{y^{8}x^{10}}{z^{4}}$$

Expand

$$\frac{y^{8}x^{10}}{z^{4}}$$

Solution Steps

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

$$\left(\frac{z^{-3}y^{4}x^{5}}{\frac{1}{z}}\right)^{2}$$

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

$$\left(\frac{y^{4}x^{5}}{z^{2}}\right)^{2}$$

To raise \frac{y^{4}x^{5}}{z^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(y^{4}x^{5}\right)^{2}}{\left(z^{2}\right)^{2}}$$

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

$$\frac{\left(y^{4}x^{5}\right)^{2}}{z^{4}}$$

Expand \left(y^{4}x^{5}\right)^{2}.

$$\frac{\left(y^{4}\right)^{2}\left(x^{5}\right)^{2}}{z^{4}}$$

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

$$\frac{y^{8}\left(x^{5}\right)^{2}}{z^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{y^{8}x^{10}}{z^{4}}$$