Solve (-2R^{2}s)^5(3R^-1s^3)^2

$$( - 2 R ^ { 2 } s ) ^ { 5 } ( 3 R ^ { - 1 } s ^ { 3 } ) ^ { 2 }$$

Evaluate

$$-288R^{8}s^{11}$$

Solution Steps

Expand \left(-2R^{2}s\right)^{5}.

$$\left(-2\right)^{5}\left(R^{2}\right)^{5}s^{5}\times \left(3R^{-1}s^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\left(-2\right)^{5}R^{10}s^{5}\times \left(3R^{-1}s^{3}\right)^{2}$$

Calculate -2 to the power of 5 and get -32.

$$-32R^{10}s^{5}\times \left(3R^{-1}s^{3}\right)^{2}$$

Expand \left(3R^{-1}s^{3}\right)^{2}.

$$-32R^{10}s^{5}\times 3^{2}\left(R^{-1}\right)^{2}\left(s^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$-32R^{10}s^{5}\times 3^{2}R^{-2}\left(s^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$-32R^{10}s^{5}\times 3^{2}R^{-2}s^{6}$$

Calculate 3 to the power of 2 and get 9.

$$-32R^{10}s^{5}\times 9R^{-2}s^{6}$$

Multiply -32 and 9 to get -288.

$$-288R^{10}s^{5}R^{-2}s^{6}$$

To multiply powers of the same base, add their exponents. Add 10 and -2 to get 8.

$$-288R^{8}s^{5}s^{6}$$

To multiply powers of the same base, add their exponents. Add 5 and 6 to get 11.

$$-288R^{8}s^{11}$$

Expand

$$-288R^{8}s^{11}$$

Solution Steps

Expand \left(-2R^{2}s\right)^{5}.

$$\left(-2\right)^{5}\left(R^{2}\right)^{5}s^{5}\times \left(3R^{-1}s^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\left(-2\right)^{5}R^{10}s^{5}\times \left(3R^{-1}s^{3}\right)^{2}$$

Calculate -2 to the power of 5 and get -32.

$$-32R^{10}s^{5}\times \left(3R^{-1}s^{3}\right)^{2}$$

Expand \left(3R^{-1}s^{3}\right)^{2}.

$$-32R^{10}s^{5}\times 3^{2}\left(R^{-1}\right)^{2}\left(s^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$-32R^{10}s^{5}\times 3^{2}R^{-2}\left(s^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$-32R^{10}s^{5}\times 3^{2}R^{-2}s^{6}$$

Calculate 3 to the power of 2 and get 9.

$$-32R^{10}s^{5}\times 9R^{-2}s^{6}$$

Multiply -32 and 9 to get -288.

$$-288R^{10}s^{5}R^{-2}s^{6}$$

To multiply powers of the same base, add their exponents. Add 10 and -2 to get 8.

$$-288R^{8}s^{5}s^{6}$$

To multiply powers of the same base, add their exponents. Add 5 and 6 to get 11.

$$-288R^{8}s^{11}$$