Solve 3a(-ab^{2})^{2}]^2-[(-1/2a)^3(-2ab^3)]^2

$$3 a ( - a b ^ { 2 } ) ^ { 2 } ] ^ { 2 } - [ ( - \frac { 1 } { 2 } a ) ^ { 3 } ( - 2 a b ^ { 3 } ) ] ^ { 2 }$$

Evaluate

$$3a^{3}b^{4}$$

Solution Steps

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

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

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

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

Calculate -a to the power of 2 and get a^{2}.

$$3aa^{2}b^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$3a^{3}b^{4}$$

Expand

$$3a^{3}b^{4}$$

Solution Steps

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

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

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

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

Calculate -a to the power of 2 and get a^{2}.

$$3aa^{2}b^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$3a^{3}b^{4}$$