Solve (7/5a^{6}b^{4}+1/4a^{6}b^{4}-9/10a^{6}b^{4}):(5/8a^{2}b^{2}-frac{1}{2}a^{2}b^2+frac{1}{4}a^2b^2):(-2a^2)

$$( \frac { 7 } { 5 } a ^ { 6 } b ^ { 4 } + \frac { 1 } { 4 } a ^ { 6 } b ^ { 4 } - \frac { 9 } { 10 } a ^ { 6 } b ^ { 4 } ) : ( \frac { 5 } { 8 } a ^ { 2 } b ^ { 2 } - \frac { 1 } { 2 } a ^ { 2 } b ^ { 2 } + \frac { 1 } { 4 } a ^ { 2 } b ^ { 2 } ) : ( - 2 a ^ { 2 } )$$

Evaluate

$$-\left(ab\right)^{2}$$

Solution Steps

Express \frac{\frac{\frac{7}{5}a^{6}b^{4}+\frac{1}{4}a^{6}b^{4}-\frac{9}{10}a^{6}b^{4}}{\frac{5}{8}a^{2}b^{2}-\frac{1}{2}a^{2}b^{2}+\frac{1}{4}a^{2}b^{2}}}{-2a^{2}} as a single fraction.

$$\frac{\frac{7}{5}a^{6}b^{4}+\frac{1}{4}a^{6}b^{4}-\frac{9}{10}a^{6}b^{4}}{\left(\frac{5}{8}a^{2}b^{2}-\frac{1}{2}a^{2}b^{2}+\frac{1}{4}a^{2}b^{2}\right)\left(-2\right)a^{2}}$$

Combine \frac{7}{5}a^{6}b^{4} and \frac{1}{4}a^{6}b^{4} to get \frac{33}{20}a^{6}b^{4}.

$$\frac{\frac{33}{20}a^{6}b^{4}-\frac{9}{10}a^{6}b^{4}}{\left(\frac{5}{8}a^{2}b^{2}-\frac{1}{2}a^{2}b^{2}+\frac{1}{4}a^{2}b^{2}\right)\left(-2\right)a^{2}}$$

Combine \frac{33}{20}a^{6}b^{4} and -\frac{9}{10}a^{6}b^{4} to get \frac{3}{4}a^{6}b^{4}.

$$\frac{\frac{3}{4}a^{6}b^{4}}{\left(\frac{5}{8}a^{2}b^{2}-\frac{1}{2}a^{2}b^{2}+\frac{1}{4}a^{2}b^{2}\right)\left(-2\right)a^{2}}$$

Combine \frac{5}{8}a^{2}b^{2} and -\frac{1}{2}a^{2}b^{2} to get \frac{1}{8}a^{2}b^{2}.

$$\frac{\frac{3}{4}a^{6}b^{4}}{\left(\frac{1}{8}a^{2}b^{2}+\frac{1}{4}a^{2}b^{2}\right)\left(-2\right)a^{2}}$$

Combine \frac{1}{8}a^{2}b^{2} and \frac{1}{4}a^{2}b^{2} to get \frac{3}{8}a^{2}b^{2}.

$$\frac{\frac{3}{4}a^{6}b^{4}}{\frac{3}{8}a^{2}b^{2}\left(-2\right)a^{2}}$$

Multiply \frac{3}{8} and -2 to get -\frac{3}{4}.

$$\frac{\frac{3}{4}a^{6}b^{4}}{-\frac{3}{4}a^{2}b^{2}a^{2}}$$

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

$$\frac{\frac{3}{4}a^{6}b^{4}}{-\frac{3}{4}a^{4}b^{2}}$$

Cancel out b^{2}a^{4} in both numerator and denominator.

$$\frac{\frac{3}{4}a^{2}b^{2}}{-\frac{3}{4}}$$

Cancel out -\frac{3}{4} and -\frac{3}{4}.

$$-a^{2}b^{2}$$

Expand

$$-\left(ab\right)^{2}$$

Solution Steps

Express \frac{\frac{\frac{7}{5}a^{6}b^{4}+\frac{1}{4}a^{6}b^{4}-\frac{9}{10}a^{6}b^{4}}{\frac{5}{8}a^{2}b^{2}-\frac{1}{2}a^{2}b^{2}+\frac{1}{4}a^{2}b^{2}}}{-2a^{2}} as a single fraction.

$$\frac{\frac{7}{5}a^{6}b^{4}+\frac{1}{4}a^{6}b^{4}-\frac{9}{10}a^{6}b^{4}}{\left(\frac{5}{8}a^{2}b^{2}-\frac{1}{2}a^{2}b^{2}+\frac{1}{4}a^{2}b^{2}\right)\left(-2\right)a^{2}}$$

Combine \frac{7}{5}a^{6}b^{4} and \frac{1}{4}a^{6}b^{4} to get \frac{33}{20}a^{6}b^{4}.

$$\frac{\frac{33}{20}a^{6}b^{4}-\frac{9}{10}a^{6}b^{4}}{\left(\frac{5}{8}a^{2}b^{2}-\frac{1}{2}a^{2}b^{2}+\frac{1}{4}a^{2}b^{2}\right)\left(-2\right)a^{2}}$$

Combine \frac{33}{20}a^{6}b^{4} and -\frac{9}{10}a^{6}b^{4} to get \frac{3}{4}a^{6}b^{4}.

$$\frac{\frac{3}{4}a^{6}b^{4}}{\left(\frac{5}{8}a^{2}b^{2}-\frac{1}{2}a^{2}b^{2}+\frac{1}{4}a^{2}b^{2}\right)\left(-2\right)a^{2}}$$

Combine \frac{5}{8}a^{2}b^{2} and -\frac{1}{2}a^{2}b^{2} to get \frac{1}{8}a^{2}b^{2}.

$$\frac{\frac{3}{4}a^{6}b^{4}}{\left(\frac{1}{8}a^{2}b^{2}+\frac{1}{4}a^{2}b^{2}\right)\left(-2\right)a^{2}}$$

Combine \frac{1}{8}a^{2}b^{2} and \frac{1}{4}a^{2}b^{2} to get \frac{3}{8}a^{2}b^{2}.

$$\frac{\frac{3}{4}a^{6}b^{4}}{\frac{3}{8}a^{2}b^{2}\left(-2\right)a^{2}}$$

Multiply \frac{3}{8} and -2 to get -\frac{3}{4}.

$$\frac{\frac{3}{4}a^{6}b^{4}}{-\frac{3}{4}a^{2}b^{2}a^{2}}$$

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

$$\frac{\frac{3}{4}a^{6}b^{4}}{-\frac{3}{4}a^{4}b^{2}}$$

Cancel out b^{2}a^{4} in both numerator and denominator.

$$\frac{\frac{3}{4}a^{2}b^{2}}{-\frac{3}{4}}$$

Cancel out -\frac{3}{4} and -\frac{3}{4}.

$$-a^{2}b^{2}$$