Solve (u^2/-5v^3)^3

$$( \frac { u ^ { 2 } } { - 5 v ^ { 3 } } ) ^ { 3 }$$

Evaluate

$$-\frac{u^{6}}{125v^{9}}$$

Solution Steps

To raise \frac{u^{2}}{-5v^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(u^{2}\right)^{3}}{\left(-5v^{3}\right)^{3}}$$

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

$$\frac{u^{6}}{\left(-5v^{3}\right)^{3}}$$

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

$$\frac{u^{6}}{\left(-5\right)^{3}\left(v^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{u^{6}}{\left(-5\right)^{3}v^{9}}$$

Calculate -5 to the power of 3 and get -125.

$$\frac{u^{6}}{-125v^{9}}$$

Expand

$$-\frac{u^{6}}{125v^{9}}$$

Solution Steps

To raise \frac{u^{2}}{-5v^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(u^{2}\right)^{3}}{\left(-5v^{3}\right)^{3}}$$

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

$$\frac{u^{6}}{\left(-5v^{3}\right)^{3}}$$

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

$$\frac{u^{6}}{\left(-5\right)^{3}\left(v^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{u^{6}}{\left(-5\right)^{3}v^{9}}$$

Calculate -5 to the power of 3 and get -125.

$$\frac{u^{6}}{-125v^{9}}$$