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

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

Evaluate

$$-\frac{9u^{6}}{25}$$

Solution Steps

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

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

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$-\frac{\frac{1}{25}}{\left(3u^{3}\right)^{-2}}$$

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

$$-\frac{\frac{1}{25}}{3^{-2}\left(u^{3}\right)^{-2}}$$

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

$$-\frac{\frac{1}{25}}{3^{-2}u^{-6}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$-\frac{\frac{1}{25}}{\frac{1}{9}u^{-6}}$$

Express \frac{\frac{1}{25}}{\frac{1}{9}u^{-6}} as a single fraction.

$$-\frac{1}{25\times \frac{1}{9}u^{-6}}$$

Multiply 25 and \frac{1}{9} to get \frac{25}{9}.

$$-\frac{1}{\frac{25}{9}u^{-6}}$$

Expand

$$-\frac{9u^{6}}{25}$$

Solution Steps

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

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

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$-\frac{\frac{1}{25}}{\left(3u^{3}\right)^{-2}}$$

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

$$-\frac{\frac{1}{25}}{3^{-2}\left(u^{3}\right)^{-2}}$$

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

$$-\frac{\frac{1}{25}}{3^{-2}u^{-6}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$-\frac{\frac{1}{25}}{\frac{1}{9}u^{-6}}$$

Express \frac{\frac{1}{25}}{\frac{1}{9}u^{-6}} as a single fraction.

$$-\frac{1}{25\times \frac{1}{9}u^{-6}}$$

Multiply 25 and \frac{1}{9} to get \frac{25}{9}.

$$-\frac{1}{\frac{25}{9}u^{-6}}$$