Solve (4r^10s^-4)^2

$$( 4 r ^ { 10 } s ^ { - 4 } ) ^ { 2 }$$

Evaluate

$$\frac{16r^{20}}{s^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4r^{10}s^{-4}\right)^{2}$$

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

$$4^{2}\left(r^{10}\right)^{2}\left(s^{-4}\right)^{2}$$

Raise 4 to the power 2.

$$16\left(r^{10}\right)^{2}\left(s^{-4}\right)^{2}$$

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

$$16r^{10\times 2}s^{-4\times 2}$$

Multiply 10 times 2.

$$16r^{20}s^{-4\times 2}$$

Multiply -4 times 2.

$$16r^{20}\times \frac{1}{s^{8}}$$

Expand

$$\frac{16r^{20}}{s^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4r^{10}s^{-4}\right)^{2}$$

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

$$4^{2}\left(r^{10}\right)^{2}\left(s^{-4}\right)^{2}$$

Raise 4 to the power 2.

$$16\left(r^{10}\right)^{2}\left(s^{-4}\right)^{2}$$

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

$$16r^{10\times 2}s^{-4\times 2}$$

Multiply 10 times 2.

$$16r^{20}s^{-4\times 2}$$

Multiply -4 times 2.

$$16r^{20}\times \frac{1}{s^{8}}$$