Solve (6n^{5}p^4)^4(-3n^3p^-7)

$$( 6 n ^ { 5 } p ^ { 4 } ) ^ { 4 } ( - 3 n ^ { 3 } p ^ { - 7 } )$$

Evaluate

$$-3888p^{9}n^{23}$$

Solution Steps

Expand \left(6n^{5}p^{4}\right)^{4}.

$$6^{4}\left(n^{5}\right)^{4}\left(p^{4}\right)^{4}\left(-3\right)n^{3}p^{-7}$$

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

$$6^{4}n^{20}\left(p^{4}\right)^{4}\left(-3\right)n^{3}p^{-7}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$6^{4}n^{20}p^{16}\left(-3\right)n^{3}p^{-7}$$

Calculate 6 to the power of 4 and get 1296.

$$1296n^{20}p^{16}\left(-3\right)n^{3}p^{-7}$$

Multiply 1296 and -3 to get -3888.

$$-3888n^{20}p^{16}n^{3}p^{-7}$$

To multiply powers of the same base, add their exponents. Add 20 and 3 to get 23.

$$-3888n^{23}p^{16}p^{-7}$$

To multiply powers of the same base, add their exponents. Add 16 and -7 to get 9.

$$-3888n^{23}p^{9}$$

Expand

$$-3888p^{9}n^{23}$$

Solution Steps

Expand \left(6n^{5}p^{4}\right)^{4}.

$$6^{4}\left(n^{5}\right)^{4}\left(p^{4}\right)^{4}\left(-3\right)n^{3}p^{-7}$$

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

$$6^{4}n^{20}\left(p^{4}\right)^{4}\left(-3\right)n^{3}p^{-7}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$6^{4}n^{20}p^{16}\left(-3\right)n^{3}p^{-7}$$

Calculate 6 to the power of 4 and get 1296.

$$1296n^{20}p^{16}\left(-3\right)n^{3}p^{-7}$$

Multiply 1296 and -3 to get -3888.

$$-3888n^{20}p^{16}n^{3}p^{-7}$$

To multiply powers of the same base, add their exponents. Add 20 and 3 to get 23.

$$-3888n^{23}p^{16}p^{-7}$$

To multiply powers of the same base, add their exponents. Add 16 and -7 to get 9.

$$-3888n^{23}p^{9}$$