Solve (9r^20s^-3)^2

$$( 9 r ^ { 20 } s ^ { - 3 } ) ^ { 2 }$$

Evaluate

$$\frac{81r^{40}}{s^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(9r^{20}s^{-3}\right)^{2}$$

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

$$9^{2}\left(r^{20}\right)^{2}\left(s^{-3}\right)^{2}$$

Raise 9 to the power 2.

$$81\left(r^{20}\right)^{2}\left(s^{-3}\right)^{2}$$

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

$$81r^{20\times 2}s^{-3\times 2}$$

Multiply 20 times 2.

$$81r^{40}s^{-3\times 2}$$

Multiply -3 times 2.

$$81r^{40}\times \frac{1}{s^{6}}$$

Expand

$$\frac{81r^{40}}{s^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(9r^{20}s^{-3}\right)^{2}$$

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

$$9^{2}\left(r^{20}\right)^{2}\left(s^{-3}\right)^{2}$$

Raise 9 to the power 2.

$$81\left(r^{20}\right)^{2}\left(s^{-3}\right)^{2}$$

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

$$81r^{20\times 2}s^{-3\times 2}$$

Multiply 20 times 2.

$$81r^{40}s^{-3\times 2}$$

Multiply -3 times 2.

$$81r^{40}\times \frac{1}{s^{6}}$$