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

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

Evaluate

$$\frac{27x^{6}y^{9}}{8}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

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

$$\frac{27}{8}\left(x^{-2}\right)^{-3}\left(y^{-3}\right)^{-3}$$

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

$$\frac{27}{8}x^{-2\left(-3\right)}y^{-3\left(-3\right)}$$

Multiply -2 times -3.

$$\frac{27}{8}x^{6}y^{-3\left(-3\right)}$$

Multiply -3 times -3.

$$\frac{27}{8}x^{6}y^{9}$$

Expand

$$\frac{27x^{6}y^{9}}{8}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

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

$$\frac{27}{8}\left(x^{-2}\right)^{-3}\left(y^{-3}\right)^{-3}$$

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

$$\frac{27}{8}x^{-2\left(-3\right)}y^{-3\left(-3\right)}$$

Multiply -2 times -3.

$$\frac{27}{8}x^{6}y^{-3\left(-3\right)}$$

Multiply -3 times -3.

$$\frac{27}{8}x^{6}y^{9}$$