Solve -(2a^{4}b^{5})^4*(16a^4b^5)^0

$$- ( 2 a ^ { 4 } b ^ { 5 } ) ^ { 4 } \times ( 16 a ^ { 4 } b ^ { 5 } ) ^ { 0 }$$

Evaluate

$$-16a^{16}b^{20}$$

Solution Steps

Expand \left(2a^{4}b^{5}\right)^{4}.

$$\left(-2^{4}\left(a^{4}\right)^{4}\left(b^{5}\right)^{4}\right)\times \left(16a^{4}b^{5}\right)^{0}$$

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

$$\left(-2^{4}a^{16}\left(b^{5}\right)^{4}\right)\times \left(16a^{4}b^{5}\right)^{0}$$

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

$$\left(-2^{4}a^{16}b^{20}\right)\times \left(16a^{4}b^{5}\right)^{0}$$

Calculate 2 to the power of 4 and get 16.

$$\left(-16a^{16}b^{20}\right)\times \left(16a^{4}b^{5}\right)^{0}$$

Calculate 16a^{4}b^{5} to the power of 0 and get 1.

$$\left(-16a^{16}b^{20}\right)\times 1$$

Multiply -1 and 16 to get -16.

$$-16a^{16}b^{20}$$

Differentiate w.r.t. b

$$-320a^{16}b^{19}$$