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

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

Evaluate

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

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

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

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

Multiply 2 times 4.

$$x^{8}y^{-3\times 4}$$

Multiply -3 times 4.

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

Expand

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

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

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

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

Multiply 2 times 4.

$$x^{8}y^{-3\times 4}$$

Multiply -3 times 4.

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