Solve (1/3frac{1{3}x^2y})^-3

$$( \frac { 1 } { 3 \frac { 1 } { 3 } x ^ { 2 } y } ) ^ { - 3 }$$

Evaluate

$$\frac{1000y^{3}x^{6}}{27}$$

Solution Steps

Multiply 3 and 3 to get 9.

$$\left(\frac{1}{\frac{9+1}{3}x^{2}y}\right)^{-3}$$

Add 9 and 1 to get 10.

$$\left(\frac{1}{\frac{10}{3}x^{2}y}\right)^{-3}$$

To raise \frac{1}{\frac{10}{3}x^{2}y} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-3}}{\left(\frac{10}{3}x^{2}y\right)^{-3}}$$

Calculate 1 to the power of -3 and get 1.

$$\frac{1}{\left(\frac{10}{3}x^{2}y\right)^{-3}}$$

Expand \left(\frac{10}{3}x^{2}y\right)^{-3}.

$$\frac{1}{\left(\frac{10}{3}\right)^{-3}\left(x^{2}\right)^{-3}y^{-3}}$$

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

$$\frac{1}{\left(\frac{10}{3}\right)^{-3}x^{-6}y^{-3}}$$

Calculate \frac{10}{3} to the power of -3 and get \frac{27}{1000}.

$$\frac{1}{\frac{27}{1000}x^{-6}y^{-3}}$$

Expand

$$\frac{1000y^{3}x^{6}}{27}$$

Solution Steps

Multiply 3 and 3 to get 9.

$$\left(\frac{1}{\frac{9+1}{3}x^{2}y}\right)^{-3}$$

Add 9 and 1 to get 10.

$$\left(\frac{1}{\frac{10}{3}x^{2}y}\right)^{-3}$$

To raise \frac{1}{\frac{10}{3}x^{2}y} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-3}}{\left(\frac{10}{3}x^{2}y\right)^{-3}}$$

Calculate 1 to the power of -3 and get 1.

$$\frac{1}{\left(\frac{10}{3}x^{2}y\right)^{-3}}$$

Expand \left(\frac{10}{3}x^{2}y\right)^{-3}.

$$\frac{1}{\left(\frac{10}{3}\right)^{-3}\left(x^{2}\right)^{-3}y^{-3}}$$

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

$$\frac{1}{\left(\frac{10}{3}\right)^{-3}x^{-6}y^{-3}}$$

Calculate \frac{10}{3} to the power of -3 and get \frac{27}{1000}.

$$\frac{1}{\frac{27}{1000}x^{-6}y^{-3}}$$