Solve (x^3/y)^2

$$( \frac { x ^ { 3 } } { y } ) ^ { 2 }$$

Evaluate

$$\frac{x^{6}}{y^{2}}$$

Steps for Raising the Quotient to a Power

Use the rules of exponents to simplify the expression.

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

To raise the quotient of two numbers to a power, raise each number to the power and then divide.

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

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

$$\frac{x^{3\times 2}}{y^{2}}$$

Multiply 3 times 2.

$$\frac{x^{6}}{y^{2}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(x^{3}\times \frac{1}{y}\right)^{2}$$

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

$$\left(x^{3}\right)^{2}\times \left(\frac{1}{y}\right)^{2}$$

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

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

Multiply 3 times 2.

$$x^{6}y^{-2}$$

Multiply -1 times 2.

$$x^{6}\times \frac{1}{y^{2}}$$

Expand

$$\frac{x^{6}}{y^{2}}$$

Steps for Raising the Quotient to a Power

Use the rules of exponents to simplify the expression.

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

To raise the quotient of two numbers to a power, raise each number to the power and then divide.

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

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

$$\frac{x^{3\times 2}}{y^{2}}$$

Multiply 3 times 2.

$$\frac{x^{6}}{y^{2}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(x^{3}\times \frac{1}{y}\right)^{2}$$

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

$$\left(x^{3}\right)^{2}\times \left(\frac{1}{y}\right)^{2}$$

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

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

Multiply 3 times 2.

$$x^{6}y^{-2}$$

Multiply -1 times 2.

$$x^{6}\times \frac{1}{y^{2}}$$