Solve (x^4y^6)^-9

$$( x ^ { 4 } y ^ { 6 } ) ^ { - 9 }$$

Evaluate

$$\frac{1}{x^{36}y^{54}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(x^{4}y^{6}\right)^{-9}$$

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

$$\left(x^{4}\right)^{-9}\left(y^{6}\right)^{-9}$$

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

$$x^{4\left(-9\right)}y^{6\left(-9\right)}$$

Multiply 4 times -9.

$$\frac{1}{x^{36}}y^{6\left(-9\right)}$$

Multiply 6 times -9.

$$\frac{1}{x^{36}}\times \frac{1}{y^{54}}$$

Expand

$$\frac{1}{x^{36}y^{54}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(x^{4}y^{6}\right)^{-9}$$

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

$$\left(x^{4}\right)^{-9}\left(y^{6}\right)^{-9}$$

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

$$x^{4\left(-9\right)}y^{6\left(-9\right)}$$

Multiply 4 times -9.

$$\frac{1}{x^{36}}y^{6\left(-9\right)}$$

Multiply 6 times -9.

$$\frac{1}{x^{36}}\times \frac{1}{y^{54}}$$