Solve (4s^3r^-5t^-2)^3

$$( 4 s ^ { 3 } r ^ { - 5 } t ^ { - 2 } ) ^ { 3 }$$

Evaluate

$$\frac{64s^{9}}{t^{6}r^{15}}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(4s^{3}r^{-5}t^{-2}\right)^{3}$$

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

$$4^{3}\left(s^{3}\right)^{3}\left(r^{-5}\right)^{3}\left(t^{-2}\right)^{3}$$

Raise 4 to the power 3.

$$64\left(s^{3}\right)^{3}\left(r^{-5}\right)^{3}\left(t^{-2}\right)^{3}$$

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

$$64s^{3\times 3}r^{-5\times 3}t^{-2\times 3}$$

Multiply 3 times 3.

$$64s^{9}r^{-5\times 3}t^{-2\times 3}$$

Multiply -5 times 3.

$$64s^{9}\times \frac{1}{r^{15}}t^{-2\times 3}$$

Multiply -2 times 3.

$$64s^{9}\times \frac{1}{r^{15}}\times \frac{1}{t^{6}}$$

Expand

$$\frac{64s^{9}}{t^{6}r^{15}}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(4s^{3}r^{-5}t^{-2}\right)^{3}$$

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

$$4^{3}\left(s^{3}\right)^{3}\left(r^{-5}\right)^{3}\left(t^{-2}\right)^{3}$$

Raise 4 to the power 3.

$$64\left(s^{3}\right)^{3}\left(r^{-5}\right)^{3}\left(t^{-2}\right)^{3}$$

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

$$64s^{3\times 3}r^{-5\times 3}t^{-2\times 3}$$

Multiply 3 times 3.

$$64s^{9}r^{-5\times 3}t^{-2\times 3}$$

Multiply -5 times 3.

$$64s^{9}\times \frac{1}{r^{15}}t^{-2\times 3}$$

Multiply -2 times 3.

$$64s^{9}\times \frac{1}{r^{15}}\times \frac{1}{t^{6}}$$