Solve {left(-frac{7/5bx^3right)}^{2}}{left(-2x^2right)^3}-{left(-5/7right)}^{2}+-b^2--frac{4/7{b}^4{x}^2}{-8/21{b}^2{x}^2}

$$\frac{ { \left(- \frac{ 7 }{ 5 } b { x }^{ 3 } \right) }^{ 2 } }{ { \left(-2 { x }^{ 2 } \right) }^{ 3 } } - { \left(- \frac{ 5 }{ 7 } \right) }^{ 2 } +- { b }^{ 2 } - \frac{ - \frac{ 4 }{ 7 } { b }^{ 4 } { x }^{ 2 } }{ - \frac{ 8 }{ 21 } { b }^{ 2 } { x }^{ 2 } }$$

Evaluate

$$-\frac{549b^{2}}{200}-\frac{25}{49}$$

Solution Steps

Expand \left(-\frac{7}{5}bx^{3}\right)^{2}.

$$\frac{\left(-\frac{7}{5}\right)^{2}b^{2}\left(x^{3}\right)^{2}}{\left(-2x^{2}\right)^{3}}-\left(-\frac{5}{7}\right)^{2}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

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

$$\frac{\left(-\frac{7}{5}\right)^{2}b^{2}x^{6}}{\left(-2x^{2}\right)^{3}}-\left(-\frac{5}{7}\right)^{2}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

Calculate -\frac{7}{5} to the power of 2 and get \frac{49}{25}.

$$\frac{\frac{49}{25}b^{2}x^{6}}{\left(-2x^{2}\right)^{3}}-\left(-\frac{5}{7}\right)^{2}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

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

$$\frac{\frac{49}{25}b^{2}x^{6}}{\left(-2\right)^{3}\left(x^{2}\right)^{3}}-\left(-\frac{5}{7}\right)^{2}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

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

$$\frac{\frac{49}{25}b^{2}x^{6}}{\left(-2\right)^{3}x^{6}}-\left(-\frac{5}{7}\right)^{2}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{\frac{49}{25}b^{2}x^{6}}{-8x^{6}}-\left(-\frac{5}{7}\right)^{2}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

Cancel out x^{6} in both numerator and denominator.

$$\frac{\frac{49}{25}b^{2}}{-8}-\left(-\frac{5}{7}\right)^{2}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

Divide \frac{49}{25}b^{2} by -8 to get -\frac{49}{200}b^{2}.

$$-\frac{49}{200}b^{2}-\left(-\frac{5}{7}\right)^{2}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

Calculate -\frac{5}{7} to the power of 2 and get \frac{25}{49}.

$$-\frac{49}{200}b^{2}-\frac{25}{49}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

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

$$-\frac{49}{200}b^{2}-\frac{25}{49}-b^{2}-\frac{-\frac{4}{7}b^{2}}{-\frac{8}{21}}$$

Divide -\frac{4}{7}b^{2} by -\frac{8}{21} by multiplying -\frac{4}{7}b^{2} by the reciprocal of -\frac{8}{21}.

$$-\frac{49}{200}b^{2}-\frac{25}{49}-b^{2}-\frac{-\frac{4}{7}b^{2}\times 21}{-8}$$

Multiply -\frac{4}{7} and 21 to get -12.

$$-\frac{49}{200}b^{2}-\frac{25}{49}-b^{2}-\frac{-12b^{2}}{-8}$$

Divide -12b^{2} by -8 to get \frac{3}{2}b^{2}.

$$-\frac{49}{200}b^{2}-\frac{25}{49}-b^{2}-\frac{3}{2}b^{2}$$

Combine -\frac{49}{200}b^{2} and -b^{2} to get -\frac{249}{200}b^{2}.

$$-\frac{249}{200}b^{2}-\frac{25}{49}-\frac{3}{2}b^{2}$$

Combine -\frac{249}{200}b^{2} and -\frac{3}{2}b^{2} to get -\frac{549}{200}b^{2}.

$$-\frac{549}{200}b^{2}-\frac{25}{49}$$

Expand

$$-\frac{549b^{2}}{200}-\frac{25}{49}$$

Solution Steps

Expand \left(-\frac{7}{5}bx^{3}\right)^{2}.

$$\frac{\left(-\frac{7}{5}\right)^{2}b^{2}\left(x^{3}\right)^{2}}{\left(-2x^{2}\right)^{3}}-\left(-\frac{5}{7}\right)^{2}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

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

$$\frac{\left(-\frac{7}{5}\right)^{2}b^{2}x^{6}}{\left(-2x^{2}\right)^{3}}-\left(-\frac{5}{7}\right)^{2}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

Calculate -\frac{7}{5} to the power of 2 and get \frac{49}{25}.

$$\frac{\frac{49}{25}b^{2}x^{6}}{\left(-2x^{2}\right)^{3}}-\left(-\frac{5}{7}\right)^{2}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

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

$$\frac{\frac{49}{25}b^{2}x^{6}}{\left(-2\right)^{3}\left(x^{2}\right)^{3}}-\left(-\frac{5}{7}\right)^{2}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

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

$$\frac{\frac{49}{25}b^{2}x^{6}}{\left(-2\right)^{3}x^{6}}-\left(-\frac{5}{7}\right)^{2}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{\frac{49}{25}b^{2}x^{6}}{-8x^{6}}-\left(-\frac{5}{7}\right)^{2}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

Cancel out x^{6} in both numerator and denominator.

$$\frac{\frac{49}{25}b^{2}}{-8}-\left(-\frac{5}{7}\right)^{2}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

Divide \frac{49}{25}b^{2} by -8 to get -\frac{49}{200}b^{2}.

$$-\frac{49}{200}b^{2}-\left(-\frac{5}{7}\right)^{2}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

Calculate -\frac{5}{7} to the power of 2 and get \frac{25}{49}.

$$-\frac{49}{200}b^{2}-\frac{25}{49}-b^{2}-\frac{-\frac{4}{7}b^{4}x^{2}}{-\frac{8}{21}b^{2}x^{2}}$$

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

$$-\frac{49}{200}b^{2}-\frac{25}{49}-b^{2}-\frac{-\frac{4}{7}b^{2}}{-\frac{8}{21}}$$

Divide -\frac{4}{7}b^{2} by -\frac{8}{21} by multiplying -\frac{4}{7}b^{2} by the reciprocal of -\frac{8}{21}.

$$-\frac{49}{200}b^{2}-\frac{25}{49}-b^{2}-\frac{-\frac{4}{7}b^{2}\times 21}{-8}$$

Multiply -\frac{4}{7} and 21 to get -12.

$$-\frac{49}{200}b^{2}-\frac{25}{49}-b^{2}-\frac{-12b^{2}}{-8}$$

Divide -12b^{2} by -8 to get \frac{3}{2}b^{2}.

$$-\frac{49}{200}b^{2}-\frac{25}{49}-b^{2}-\frac{3}{2}b^{2}$$

Combine -\frac{49}{200}b^{2} and -b^{2} to get -\frac{249}{200}b^{2}.

$$-\frac{249}{200}b^{2}-\frac{25}{49}-\frac{3}{2}b^{2}$$

Combine -\frac{249}{200}b^{2} and -\frac{3}{2}b^{2} to get -\frac{549}{200}b^{2}.

$$-\frac{549}{200}b^{2}-\frac{25}{49}$$