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

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

Evaluate

$$\frac{16y^{12}}{x^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 2 to the power 4.

$$16\left(x^{-2}\right)^{4}\left(y^{3}\right)^{4}$$

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

$$16x^{-2\times 4}y^{3\times 4}$$

Multiply -2 times 4.

$$16\times \frac{1}{x^{8}}y^{3\times 4}$$

Multiply 3 times 4.

$$16\times \frac{1}{x^{8}}y^{12}$$

Expand

$$\frac{16y^{12}}{x^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 2 to the power 4.

$$16\left(x^{-2}\right)^{4}\left(y^{3}\right)^{4}$$

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

$$16x^{-2\times 4}y^{3\times 4}$$

Multiply -2 times 4.

$$16\times \frac{1}{x^{8}}y^{3\times 4}$$

Multiply 3 times 4.

$$16\times \frac{1}{x^{8}}y^{12}$$