Solve (3x^6y^9)^-3

$$( 3 x ^ { 6 } y ^ { 9 } ) ^ { - 3 }$$

Evaluate

$$\frac{1}{27x^{18}y^{27}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power -3.

$$\frac{1}{27}\left(x^{6}\right)^{-3}\left(y^{9}\right)^{-3}$$

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

$$\frac{1}{27}x^{6\left(-3\right)}y^{9\left(-3\right)}$$

Multiply 6 times -3.

$$\frac{1}{27}\times \frac{1}{x^{18}}y^{9\left(-3\right)}$$

Multiply 9 times -3.

$$\frac{1}{27}\times \frac{1}{x^{18}}\times \frac{1}{y^{27}}$$

Expand

$$\frac{1}{27x^{18}y^{27}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power -3.

$$\frac{1}{27}\left(x^{6}\right)^{-3}\left(y^{9}\right)^{-3}$$

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

$$\frac{1}{27}x^{6\left(-3\right)}y^{9\left(-3\right)}$$

Multiply 6 times -3.

$$\frac{1}{27}\times \frac{1}{x^{18}}y^{9\left(-3\right)}$$

Multiply 9 times -3.

$$\frac{1}{27}\times \frac{1}{x^{18}}\times \frac{1}{y^{27}}$$