Solve [(-2ab^3)^2]^2

$$[ ( - 2 a b ^ { 3 } ) ^ { 2 } ] ^ { 2 }$$

Evaluate

$$16a^{4}b^{12}$$

Solution Steps

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

$$\left(\left(-2\right)^{2}a^{2}\left(b^{3}\right)^{2}\right)^{2}$$

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

$$\left(\left(-2\right)^{2}a^{2}b^{6}\right)^{2}$$

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

$$\left(4a^{2}b^{6}\right)^{2}$$

Expand \left(4a^{2}b^{6}\right)^{2}.

$$4^{2}\left(a^{2}\right)^{2}\left(b^{6}\right)^{2}$$

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

$$4^{2}a^{4}\left(b^{6}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$4^{2}a^{4}b^{12}$$

Calculate 4 to the power of 2 and get 16.

$$16a^{4}b^{12}$$

Expand

$$16a^{4}b^{12}$$

Solution Steps

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

$$\left(\left(-2\right)^{2}a^{2}\left(b^{3}\right)^{2}\right)^{2}$$

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

$$\left(\left(-2\right)^{2}a^{2}b^{6}\right)^{2}$$

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

$$\left(4a^{2}b^{6}\right)^{2}$$

Expand \left(4a^{2}b^{6}\right)^{2}.

$$4^{2}\left(a^{2}\right)^{2}\left(b^{6}\right)^{2}$$

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

$$4^{2}a^{4}\left(b^{6}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$4^{2}a^{4}b^{12}$$

Calculate 4 to the power of 2 and get 16.

$$16a^{4}b^{12}$$