Solve (1/3x^-3y)^2

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

Evaluate

$$\frac{y^{2}}{9x^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Raise \frac{1}{3} to the power 2.

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

To raise a power to another power, multiply the exponents.

$$\frac{1}{9}x^{-3\times 2}y^{2}$$

Multiply -3 times 2.

$$\frac{1}{9}\times \frac{1}{x^{6}}y^{2}$$

Expand

$$\frac{y^{2}}{9x^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Raise \frac{1}{3} to the power 2.

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

To raise a power to another power, multiply the exponents.

$$\frac{1}{9}x^{-3\times 2}y^{2}$$

Multiply -3 times 2.

$$\frac{1}{9}\times \frac{1}{x^{6}}y^{2}$$