Solve (+9/2x^4y^5)^2

$$( + \frac { 9 } { 2 } x ^ { 4 } y ^ { 5 } ) ^ { 2 }$$

Evaluate

$$\frac{81x^{8}y^{10}}{4}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{9}{2}x^{4}y^{5}\right)^{2}$$

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

$$\left(\frac{9}{2}\right)^{2}\left(x^{4}\right)^{2}\left(y^{5}\right)^{2}$$

Raise \frac{9}{2} to the power 2.

$$\frac{81}{4}\left(x^{4}\right)^{2}\left(y^{5}\right)^{2}$$

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

$$\frac{81}{4}x^{4\times 2}y^{5\times 2}$$

Multiply 4 times 2.

$$\frac{81}{4}x^{8}y^{5\times 2}$$

Multiply 5 times 2.

$$\frac{81}{4}x^{8}y^{10}$$

Expand

$$\frac{81x^{8}y^{10}}{4}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{9}{2}x^{4}y^{5}\right)^{2}$$

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

$$\left(\frac{9}{2}\right)^{2}\left(x^{4}\right)^{2}\left(y^{5}\right)^{2}$$

Raise \frac{9}{2} to the power 2.

$$\frac{81}{4}\left(x^{4}\right)^{2}\left(y^{5}\right)^{2}$$

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

$$\frac{81}{4}x^{4\times 2}y^{5\times 2}$$

Multiply 4 times 2.

$$\frac{81}{4}x^{8}y^{5\times 2}$$

Multiply 5 times 2.

$$\frac{81}{4}x^{8}y^{10}$$