Solve (-1/10x^10y^4)^2

$$( - \frac { 1 } { 10 } x ^ { 10 } y ^ { 4 } ) ^ { 2 }$$

Evaluate

$$\frac{y^{8}x^{20}}{100}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-\frac{1}{10}x^{10}y^{4}\right)^{2}$$

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

$$\left(-\frac{1}{10}\right)^{2}\left(x^{10}\right)^{2}\left(y^{4}\right)^{2}$$

Raise -\frac{1}{10} to the power 2.

$$\frac{1}{100}\left(x^{10}\right)^{2}\left(y^{4}\right)^{2}$$

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

$$\frac{1}{100}x^{10\times 2}y^{4\times 2}$$

Multiply 10 times 2.

$$\frac{1}{100}x^{20}y^{4\times 2}$$

Multiply 4 times 2.

$$\frac{1}{100}x^{20}y^{8}$$

Expand

$$\frac{y^{8}x^{20}}{100}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-\frac{1}{10}x^{10}y^{4}\right)^{2}$$

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

$$\left(-\frac{1}{10}\right)^{2}\left(x^{10}\right)^{2}\left(y^{4}\right)^{2}$$

Raise -\frac{1}{10} to the power 2.

$$\frac{1}{100}\left(x^{10}\right)^{2}\left(y^{4}\right)^{2}$$

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

$$\frac{1}{100}x^{10\times 2}y^{4\times 2}$$

Multiply 10 times 2.

$$\frac{1}{100}x^{20}y^{4\times 2}$$

Multiply 4 times 2.

$$\frac{1}{100}x^{20}y^{8}$$