Solve {l}{(-2a^{2}b^{3})^4+(-a)^8}{*(2b^4)^3}

$$\left. \begin{array} { l } { ( - 2 a ^ { 2 } b ^ { 3 } ) ^ { 4 } + ( - a ) ^ { 8 } } \\ { \times ( 2 b ^ { 4 } ) ^ { 3 } } \end{array} \right.$$

Evaluate

$$24a^{8}b^{12}$$

Solution Steps

Expand \left(-2a^{2}b^{3}\right)^{4}.

$$\left(-2\right)^{4}\left(a^{2}\right)^{4}\left(b^{3}\right)^{4}+\left(-a\right)^{8}\times \left(2b^{4}\right)^{3}$$

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

$$\left(-2\right)^{4}a^{8}\left(b^{3}\right)^{4}+\left(-a\right)^{8}\times \left(2b^{4}\right)^{3}$$

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

$$\left(-2\right)^{4}a^{8}b^{12}+\left(-a\right)^{8}\times \left(2b^{4}\right)^{3}$$

Calculate -2 to the power of 4 and get 16.

$$16a^{8}b^{12}+\left(-a\right)^{8}\times \left(2b^{4}\right)^{3}$$

Expand \left(2b^{4}\right)^{3}.

$$16a^{8}b^{12}+\left(-a\right)^{8}\times 2^{3}\left(b^{4}\right)^{3}$$

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

$$16a^{8}b^{12}+\left(-a\right)^{8}\times 2^{3}b^{12}$$

Calculate 2 to the power of 3 and get 8.

$$16a^{8}b^{12}+\left(-a\right)^{8}\times 8b^{12}$$

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

$$16a^{8}b^{12}+\left(-1\right)^{8}a^{8}\times 8b^{12}$$

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

$$16a^{8}b^{12}+1a^{8}\times 8b^{12}$$

Multiply 1 and 8 to get 8.

$$16a^{8}b^{12}+8a^{8}b^{12}$$

Combine 16a^{8}b^{12} and 8a^{8}b^{12} to get 24a^{8}b^{12}.

$$24a^{8}b^{12}$$

Expand

$$24a^{8}b^{12}$$

Solution Steps

Expand \left(-2a^{2}b^{3}\right)^{4}.

$$\left(-2\right)^{4}\left(a^{2}\right)^{4}\left(b^{3}\right)^{4}+\left(-a\right)^{8}\times \left(2b^{4}\right)^{3}$$

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

$$\left(-2\right)^{4}a^{8}\left(b^{3}\right)^{4}+\left(-a\right)^{8}\times \left(2b^{4}\right)^{3}$$

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

$$\left(-2\right)^{4}a^{8}b^{12}+\left(-a\right)^{8}\times \left(2b^{4}\right)^{3}$$

Calculate -2 to the power of 4 and get 16.

$$16a^{8}b^{12}+\left(-a\right)^{8}\times \left(2b^{4}\right)^{3}$$

Expand \left(2b^{4}\right)^{3}.

$$16a^{8}b^{12}+\left(-a\right)^{8}\times 2^{3}\left(b^{4}\right)^{3}$$

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

$$16a^{8}b^{12}+\left(-a\right)^{8}\times 2^{3}b^{12}$$

Calculate 2 to the power of 3 and get 8.

$$16a^{8}b^{12}+\left(-a\right)^{8}\times 8b^{12}$$

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

$$16a^{8}b^{12}+\left(-1\right)^{8}a^{8}\times 8b^{12}$$

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

$$16a^{8}b^{12}+1a^{8}\times 8b^{12}$$

Multiply 1 and 8 to get 8.

$$16a^{8}b^{12}+8a^{8}b^{12}$$

Combine 16a^{8}b^{12} and 8a^{8}b^{12} to get 24a^{8}b^{12}.

$$24a^{8}b^{12}$$