Solve (8s^-3t^-4)^2

$$( 8 s ^ { - 3 } t ^ { - 4 } ) ^ { 2 }$$

Evaluate

$$\frac{64}{s^{6}t^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(8s^{-3}t^{-4}\right)^{2}$$

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

$$8^{2}\left(s^{-3}\right)^{2}\left(t^{-4}\right)^{2}$$

Raise 8 to the power 2.

$$64\left(s^{-3}\right)^{2}\left(t^{-4}\right)^{2}$$

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

$$64s^{-3\times 2}t^{-4\times 2}$$

Multiply -3 times 2.

$$64\times \frac{1}{s^{6}}t^{-4\times 2}$$

Multiply -4 times 2.

$$64\times \frac{1}{s^{6}}\times \frac{1}{t^{8}}$$

Expand

$$\frac{64}{s^{6}t^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(8s^{-3}t^{-4}\right)^{2}$$

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

$$8^{2}\left(s^{-3}\right)^{2}\left(t^{-4}\right)^{2}$$

Raise 8 to the power 2.

$$64\left(s^{-3}\right)^{2}\left(t^{-4}\right)^{2}$$

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

$$64s^{-3\times 2}t^{-4\times 2}$$

Multiply -3 times 2.

$$64\times \frac{1}{s^{6}}t^{-4\times 2}$$

Multiply -4 times 2.

$$64\times \frac{1}{s^{6}}\times \frac{1}{t^{8}}$$