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

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

Evaluate

$$\frac{8y^{9}}{x^{18}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 2 to the power 3.

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

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

$$8x^{-6\times 3}y^{3\times 3}$$

Multiply -6 times 3.

$$8\times \frac{1}{x^{18}}y^{3\times 3}$$

Multiply 3 times 3.

$$8\times \frac{1}{x^{18}}y^{9}$$

Expand

$$\frac{8y^{9}}{x^{18}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 2 to the power 3.

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

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

$$8x^{-6\times 3}y^{3\times 3}$$

Multiply -6 times 3.

$$8\times \frac{1}{x^{18}}y^{3\times 3}$$

Multiply 3 times 3.

$$8\times \frac{1}{x^{18}}y^{9}$$