Solve =3/4a^{2}x^{2}(-1/2abx)^{2}]:(-1/4a^{2}4a^{2}x^{2}+1/2a^{2}bx)^{2}-frac{4}{9}a^{2}b^4x^2:(-frac{2}{3}a^2b^4)=

$$= \frac { 3 } { 4 } a ^ { 2 } x ^ { 2 } ( - \frac { 1 } { 2 } a b x ) ^ { 2 } ] : ( - \frac { 1 } { 4 } a ^ { 2 } 4 a ^ { 2 } x ^ { 2 } + \frac { 1 } { 2 } a ^ { 2 } b x ) ^ { 2 } - \frac { 4 } { 9 } a ^ { 2 } b ^ { 4 } x ^ { 2 } : ( - \frac { 2 } { 3 } a ^ { 2 } b ^ { 4 } ) =$$

Evaluate

$$\frac{3b^{2}\left(ax\right)^{4}}{16}$$

Solution Steps

Expand \left(-\frac{1}{2}abx\right)^{2}.

$$\frac{3}{4}a^{2}x^{2}\left(-\frac{1}{2}\right)^{2}a^{2}b^{2}x^{2}$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{3}{4}a^{2}x^{2}\times \frac{1}{4}a^{2}b^{2}x^{2}$$

Multiply \frac{3}{4} and \frac{1}{4} to get \frac{3}{16}.

$$\frac{3}{16}a^{2}x^{2}a^{2}b^{2}x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{3}{16}a^{4}x^{2}b^{2}x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{3}{16}a^{4}x^{4}b^{2}$$

Expand

$$\frac{3b^{2}\left(ax\right)^{4}}{16}$$

Solution Steps

Expand \left(-\frac{1}{2}abx\right)^{2}.

$$\frac{3}{4}a^{2}x^{2}\left(-\frac{1}{2}\right)^{2}a^{2}b^{2}x^{2}$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{3}{4}a^{2}x^{2}\times \frac{1}{4}a^{2}b^{2}x^{2}$$

Multiply \frac{3}{4} and \frac{1}{4} to get \frac{3}{16}.

$$\frac{3}{16}a^{2}x^{2}a^{2}b^{2}x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{3}{16}a^{4}x^{2}b^{2}x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{3}{16}a^{4}x^{4}b^{2}$$