Solve (r^-3s^4)^2

$$( r ^ { - 3 } s ^ { 4 } ) ^ { 2 }$$

Evaluate

$$\frac{s^{8}}{r^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(r^{-3}s^{4}\right)^{2}$$

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

$$\left(r^{-3}\right)^{2}\left(s^{4}\right)^{2}$$

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

$$r^{-3\times 2}s^{4\times 2}$$

Multiply -3 times 2.

$$\frac{1}{r^{6}}s^{4\times 2}$$

Multiply 4 times 2.

$$\frac{1}{r^{6}}s^{8}$$

Expand

$$\frac{s^{8}}{r^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(r^{-3}s^{4}\right)^{2}$$

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

$$\left(r^{-3}\right)^{2}\left(s^{4}\right)^{2}$$

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

$$r^{-3\times 2}s^{4\times 2}$$

Multiply -3 times 2.

$$\frac{1}{r^{6}}s^{4\times 2}$$

Multiply 4 times 2.

$$\frac{1}{r^{6}}s^{8}$$