Solve (2/3x^2y^-4)^-2

$$( \frac { 2 } { 3 } x ^ { 2 } y ^ { - 4 } ) ^ { - 2 }$$

Evaluate

$$\frac{9y^{8}}{4x^{4}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{2}{3}x^{2}y^{-4}\right)^{-2}$$

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

$$\left(\frac{2}{3}\right)^{-2}\left(x^{2}\right)^{-2}\left(y^{-4}\right)^{-2}$$

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

$$\frac{9}{4}\left(x^{2}\right)^{-2}\left(y^{-4}\right)^{-2}$$

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

$$\frac{9}{4}x^{2\left(-2\right)}y^{-4\left(-2\right)}$$

Multiply 2 times -2.

$$\frac{9}{4}\times \frac{1}{x^{4}}y^{-4\left(-2\right)}$$

Multiply -4 times -2.

$$\frac{9}{4}\times \frac{1}{x^{4}}y^{8}$$

Expand

$$\frac{9y^{8}}{4x^{4}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{2}{3}x^{2}y^{-4}\right)^{-2}$$

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

$$\left(\frac{2}{3}\right)^{-2}\left(x^{2}\right)^{-2}\left(y^{-4}\right)^{-2}$$

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

$$\frac{9}{4}\left(x^{2}\right)^{-2}\left(y^{-4}\right)^{-2}$$

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

$$\frac{9}{4}x^{2\left(-2\right)}y^{-4\left(-2\right)}$$

Multiply 2 times -2.

$$\frac{9}{4}\times \frac{1}{x^{4}}y^{-4\left(-2\right)}$$

Multiply -4 times -2.

$$\frac{9}{4}\times \frac{1}{x^{4}}y^{8}$$