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

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

Evaluate

$$-s^{22}r^{31}$$

Solution Steps

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

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

Calculate -r^{3} to the power of 2 and get \left(r^{3}\right)^{2}.

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

Expand \left(\left(-r^{5}\right)s^{4}\right)^{5}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\left(r^{3}\right)^{2}s^{2}\left(-r^{5}\right)^{5}s^{20}$$

To multiply powers of the same base, add their exponents. Add 2 and 20 to get 22.

$$\left(r^{3}\right)^{2}s^{22}\left(-r^{5}\right)^{5}$$

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

$$r^{6}s^{22}\left(-r^{5}\right)^{5}$$

Expand \left(-r^{5}\right)^{5}.

$$r^{6}s^{22}\left(-1\right)^{5}\left(r^{5}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$r^{6}s^{22}\left(-1\right)^{5}r^{25}$$

Calculate -1 to the power of 5 and get -1.

$$r^{6}s^{22}\left(-1\right)r^{25}$$

To multiply powers of the same base, add their exponents. Add 6 and 25 to get 31.

$$r^{31}s^{22}\left(-1\right)$$

Expand

$$-s^{22}r^{31}$$

Solution Steps

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

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

Calculate -r^{3} to the power of 2 and get \left(r^{3}\right)^{2}.

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

Expand \left(\left(-r^{5}\right)s^{4}\right)^{5}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\left(r^{3}\right)^{2}s^{2}\left(-r^{5}\right)^{5}s^{20}$$

To multiply powers of the same base, add their exponents. Add 2 and 20 to get 22.

$$\left(r^{3}\right)^{2}s^{22}\left(-r^{5}\right)^{5}$$

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

$$r^{6}s^{22}\left(-r^{5}\right)^{5}$$

Expand \left(-r^{5}\right)^{5}.

$$r^{6}s^{22}\left(-1\right)^{5}\left(r^{5}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$r^{6}s^{22}\left(-1\right)^{5}r^{25}$$

Calculate -1 to the power of 5 and get -1.

$$r^{6}s^{22}\left(-1\right)r^{25}$$

To multiply powers of the same base, add their exponents. Add 6 and 25 to get 31.

$$r^{31}s^{22}\left(-1\right)$$