Solve (-7x^3y^2/xz^3)^2

$$( \frac { - 7 x ^ { 3 } y ^ { 2 } } { x z ^ { 3 } } ) ^ { 2 }$$

Evaluate

$$\frac{49\left(xy\right)^{4}}{z^{6}}$$

Solution Steps

Cancel out x in both numerator and denominator.

$$\left(\frac{-7x^{2}y^{2}}{z^{3}}\right)^{2}$$

To raise \frac{-7x^{2}y^{2}}{z^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-7x^{2}y^{2}\right)^{2}}{\left(z^{3}\right)^{2}}$$

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

$$\frac{\left(-7x^{2}y^{2}\right)^{2}}{z^{6}}$$

Expand \left(-7x^{2}y^{2}\right)^{2}.

$$\frac{\left(-7\right)^{2}\left(x^{2}\right)^{2}\left(y^{2}\right)^{2}}{z^{6}}$$

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

$$\frac{\left(-7\right)^{2}x^{4}\left(y^{2}\right)^{2}}{z^{6}}$$

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

$$\frac{\left(-7\right)^{2}x^{4}y^{4}}{z^{6}}$$

Calculate -7 to the power of 2 and get 49.

$$\frac{49x^{4}y^{4}}{z^{6}}$$

Expand

$$\frac{49\left(xy\right)^{4}}{z^{6}}$$

Solution Steps

Cancel out x in both numerator and denominator.

$$\left(\frac{-7x^{2}y^{2}}{z^{3}}\right)^{2}$$

To raise \frac{-7x^{2}y^{2}}{z^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-7x^{2}y^{2}\right)^{2}}{\left(z^{3}\right)^{2}}$$

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

$$\frac{\left(-7x^{2}y^{2}\right)^{2}}{z^{6}}$$

Expand \left(-7x^{2}y^{2}\right)^{2}.

$$\frac{\left(-7\right)^{2}\left(x^{2}\right)^{2}\left(y^{2}\right)^{2}}{z^{6}}$$

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

$$\frac{\left(-7\right)^{2}x^{4}\left(y^{2}\right)^{2}}{z^{6}}$$

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

$$\frac{\left(-7\right)^{2}x^{4}y^{4}}{z^{6}}$$

Calculate -7 to the power of 2 and get 49.

$$\frac{49x^{4}y^{4}}{z^{6}}$$