Solve (3x^-6y^3)^-2

$$( 3 x ^ { - 6 } y ^ { 3 } ) ^ { - 2 }$$

Evaluate

$$\frac{x^{12}}{9y^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(3x^{-6}y^{3}\right)^{-2}$$

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

$$3^{-2}\left(x^{-6}\right)^{-2}\left(y^{3}\right)^{-2}$$

Raise 3 to the power -2.

$$\frac{1}{9}\left(x^{-6}\right)^{-2}\left(y^{3}\right)^{-2}$$

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

$$\frac{1}{9}x^{-6\left(-2\right)}y^{3\left(-2\right)}$$

Multiply -6 times -2.

$$\frac{1}{9}x^{12}y^{3\left(-2\right)}$$

Multiply 3 times -2.

$$\frac{1}{9}x^{12}\times \frac{1}{y^{6}}$$

Expand

$$\frac{x^{12}}{9y^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(3x^{-6}y^{3}\right)^{-2}$$

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

$$3^{-2}\left(x^{-6}\right)^{-2}\left(y^{3}\right)^{-2}$$

Raise 3 to the power -2.

$$\frac{1}{9}\left(x^{-6}\right)^{-2}\left(y^{3}\right)^{-2}$$

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

$$\frac{1}{9}x^{-6\left(-2\right)}y^{3\left(-2\right)}$$

Multiply -6 times -2.

$$\frac{1}{9}x^{12}y^{3\left(-2\right)}$$

Multiply 3 times -2.

$$\frac{1}{9}x^{12}\times \frac{1}{y^{6}}$$