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

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

Evaluate

$$\frac{r^{12}}{8s^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 2 to the power -3.

$$\frac{1}{8}\left(r^{-4}\right)^{-3}\left(s^{2}\right)^{-3}$$

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

$$\frac{1}{8}r^{-4\left(-3\right)}s^{2\left(-3\right)}$$

Multiply -4 times -3.

$$\frac{1}{8}r^{12}s^{2\left(-3\right)}$$

Multiply 2 times -3.

$$\frac{1}{8}r^{12}\times \frac{1}{s^{6}}$$

Expand

$$\frac{r^{12}}{8s^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 2 to the power -3.

$$\frac{1}{8}\left(r^{-4}\right)^{-3}\left(s^{2}\right)^{-3}$$

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

$$\frac{1}{8}r^{-4\left(-3\right)}s^{2\left(-3\right)}$$

Multiply -4 times -3.

$$\frac{1}{8}r^{12}s^{2\left(-3\right)}$$

Multiply 2 times -3.

$$\frac{1}{8}r^{12}\times \frac{1}{s^{6}}$$