Solve (5xy^-3/z^5)^2

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

Evaluate

$$\frac{25x^{2}}{y^{6}z^{10}}$$

Solution Steps

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

$$\frac{\left(5xy^{-3}\right)^{2}}{\left(z^{5}\right)^{2}}$$

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

$$\frac{\left(5xy^{-3}\right)^{2}}{z^{10}}$$

Expand \left(5xy^{-3}\right)^{2}.

$$\frac{5^{2}x^{2}\left(y^{-3}\right)^{2}}{z^{10}}$$

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

$$\frac{5^{2}x^{2}y^{-6}}{z^{10}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25x^{2}y^{-6}}{z^{10}}$$

Expand

$$\frac{25x^{2}}{y^{6}z^{10}}$$

Solution Steps

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

$$\frac{\left(5xy^{-3}\right)^{2}}{\left(z^{5}\right)^{2}}$$

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

$$\frac{\left(5xy^{-3}\right)^{2}}{z^{10}}$$

Expand \left(5xy^{-3}\right)^{2}.

$$\frac{5^{2}x^{2}\left(y^{-3}\right)^{2}}{z^{10}}$$

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

$$\frac{5^{2}x^{2}y^{-6}}{z^{10}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25x^{2}y^{-6}}{z^{10}}$$