Solve left(2x^-4y^2right)^-3

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

Evaluate

$$\frac{x^{12}}{8y^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 2 to the power -3.

$$\frac{1}{8}\left(x^{-4}\right)^{-3}\left(y^{2}\right)^{-3}$$

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

$$\frac{1}{8}x^{-4\left(-3\right)}y^{2\left(-3\right)}$$

Multiply -4 times -3.

$$\frac{1}{8}x^{12}y^{2\left(-3\right)}$$

Multiply 2 times -3.

$$\frac{1}{8}x^{12}\times \frac{1}{y^{6}}$$

Expand

$$\frac{x^{12}}{8y^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 2 to the power -3.

$$\frac{1}{8}\left(x^{-4}\right)^{-3}\left(y^{2}\right)^{-3}$$

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

$$\frac{1}{8}x^{-4\left(-3\right)}y^{2\left(-3\right)}$$

Multiply -4 times -3.

$$\frac{1}{8}x^{12}y^{2\left(-3\right)}$$

Multiply 2 times -3.

$$\frac{1}{8}x^{12}\times \frac{1}{y^{6}}$$