Solve (x^3y^5/z^4)^2

$$( \frac { x ^ { 3 } y ^ { 5 } } { z ^ { 4 } } ) ^ { 2 }$$

Evaluate

$$\frac{x^{6}y^{10}}{z^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{x^{3}y^{5}}{z^{4}}\right)^{2}$$

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

$$\frac{\left(x^{3}\right)^{2}\left(y^{5}\right)^{2}}{\left(z^{4}\right)^{2}}$$

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

$$\frac{x^{3\times 2}y^{5\times 2}}{z^{4\times 2}}$$

Multiply 3 times 2.

$$\frac{x^{6}y^{5\times 2}}{z^{4\times 2}}$$

Multiply 5 times 2.

$$\frac{x^{6}y^{10}}{z^{4\times 2}}$$

Multiply 4 times 2.

$$\frac{x^{6}y^{10}}{z^{8}}$$

Expand

$$\frac{x^{6}y^{10}}{z^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{x^{3}y^{5}}{z^{4}}\right)^{2}$$

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

$$\frac{\left(x^{3}\right)^{2}\left(y^{5}\right)^{2}}{\left(z^{4}\right)^{2}}$$

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

$$\frac{x^{3\times 2}y^{5\times 2}}{z^{4\times 2}}$$

Multiply 3 times 2.

$$\frac{x^{6}y^{5\times 2}}{z^{4\times 2}}$$

Multiply 5 times 2.

$$\frac{x^{6}y^{10}}{z^{4\times 2}}$$

Multiply 4 times 2.

$$\frac{x^{6}y^{10}}{z^{8}}$$