Solve 5left(p^3right)^4left(-p^2right)^3+2{left({left(-pright)}^2right)}^4{left(-{p}^5right)}^2

$$5 { \left( { p }^{ 3 } \right) }^{ 4 } { \left(- { p }^{ 2 } \right) }^{ 3 } +2 { \left( { \left(-p \right) }^{ 2 } \right) }^{ 4 } { \left(- { p }^{ 5 } \right) }^{ 2 }$$

Evaluate

$$-3p^{18}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$5p^{12}\left(-p^{2}\right)^{3}+2\left(\left(-p\right)^{2}\right)^{4}\left(-p^{5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$5p^{12}\left(-p^{2}\right)^{3}+2\left(-p\right)^{8}\left(-p^{5}\right)^{2}$$

Calculate -p^{5} to the power of 2 and get \left(p^{5}\right)^{2}.

$$5p^{12}\left(-p^{2}\right)^{3}+2\left(-p\right)^{8}\left(p^{5}\right)^{2}$$

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

$$5p^{12}\left(-p^{2}\right)^{3}+2\left(-p\right)^{8}p^{10}$$

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

$$5p^{12}\left(-1\right)^{3}\left(p^{2}\right)^{3}+2\left(-p\right)^{8}p^{10}$$

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

$$5p^{12}\left(-1\right)^{3}p^{6}+2\left(-p\right)^{8}p^{10}$$

Calculate -1 to the power of 3 and get -1.

$$5p^{12}\left(-1\right)p^{6}+2\left(-p\right)^{8}p^{10}$$

Multiply 5 and -1 to get -5.

$$-5p^{12}p^{6}+2\left(-p\right)^{8}p^{10}$$

To multiply powers of the same base, add their exponents. Add 12 and 6 to get 18.

$$-5p^{18}+2\left(-p\right)^{8}p^{10}$$

Expand \left(-p\right)^{8}.

$$-5p^{18}+2\left(-1\right)^{8}p^{8}p^{10}$$

Calculate -1 to the power of 8 and get 1.

$$-5p^{18}+2\times 1p^{8}p^{10}$$

Multiply 2 and 1 to get 2.

$$-5p^{18}+2p^{8}p^{10}$$

To multiply powers of the same base, add their exponents. Add 8 and 10 to get 18.

$$-5p^{18}+2p^{18}$$

Combine -5p^{18} and 2p^{18} to get -3p^{18}.

$$-3p^{18}$$

Expand

$$-3p^{18}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$5p^{12}\left(-p^{2}\right)^{3}+2\left(\left(-p\right)^{2}\right)^{4}\left(-p^{5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$5p^{12}\left(-p^{2}\right)^{3}+2\left(-p\right)^{8}\left(-p^{5}\right)^{2}$$

Calculate -p^{5} to the power of 2 and get \left(p^{5}\right)^{2}.

$$5p^{12}\left(-p^{2}\right)^{3}+2\left(-p\right)^{8}\left(p^{5}\right)^{2}$$

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

$$5p^{12}\left(-p^{2}\right)^{3}+2\left(-p\right)^{8}p^{10}$$

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

$$5p^{12}\left(-1\right)^{3}\left(p^{2}\right)^{3}+2\left(-p\right)^{8}p^{10}$$

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

$$5p^{12}\left(-1\right)^{3}p^{6}+2\left(-p\right)^{8}p^{10}$$

Calculate -1 to the power of 3 and get -1.

$$5p^{12}\left(-1\right)p^{6}+2\left(-p\right)^{8}p^{10}$$

Multiply 5 and -1 to get -5.

$$-5p^{12}p^{6}+2\left(-p\right)^{8}p^{10}$$

To multiply powers of the same base, add their exponents. Add 12 and 6 to get 18.

$$-5p^{18}+2\left(-p\right)^{8}p^{10}$$

Expand \left(-p\right)^{8}.

$$-5p^{18}+2\left(-1\right)^{8}p^{8}p^{10}$$

Calculate -1 to the power of 8 and get 1.

$$-5p^{18}+2\times 1p^{8}p^{10}$$

Multiply 2 and 1 to get 2.

$$-5p^{18}+2p^{8}p^{10}$$

To multiply powers of the same base, add their exponents. Add 8 and 10 to get 18.

$$-5p^{18}+2p^{18}$$

Combine -5p^{18} and 2p^{18} to get -3p^{18}.

$$-3p^{18}$$