Solve (5x^3z/y^2)^2

$$( \frac { 5 x ^ { 3 } z } { y ^ { 2 } } ) ^ { 2 }$$

Evaluate

$$\frac{25z^{2}x^{6}}{y^{4}}$$

Solution Steps

To raise \frac{5x^{3}z}{y^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Expand \left(5x^{3}z\right)^{2}.

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

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

$$\frac{5^{2}x^{6}z^{2}}{y^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25x^{6}z^{2}}{y^{4}}$$

Expand

$$\frac{25z^{2}x^{6}}{y^{4}}$$

Solution Steps

To raise \frac{5x^{3}z}{y^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Expand \left(5x^{3}z\right)^{2}.

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

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

$$\frac{5^{2}x^{6}z^{2}}{y^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25x^{6}z^{2}}{y^{4}}$$