Solve 5b/40a^3b^2+4aa^2/40a^3{b^2}

$$\frac{ 5b }{ 40 { a }^{ 3 } { b }^{ 2 } } + \frac{ 4a { a }^{ 2 } }{ 40 { a }^{ 3 } { b }^{ 2 } }$$

Evaluate

$$\frac{1}{10b^{2}}+\frac{1}{8ba^{3}}$$

Solution Steps

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

$$\frac{5b}{40a^{3}b^{2}}+\frac{4a^{3}}{40a^{3}b^{2}}$$

Cancel out 5b in both numerator and denominator.

$$\frac{1}{8ba^{3}}+\frac{4a^{3}}{40a^{3}b^{2}}$$

Cancel out 4a^{3} in both numerator and denominator.

$$\frac{1}{8ba^{3}}+\frac{1}{10b^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8ba^{3} and 10b^{2} is 40b^{2}a^{3}. Multiply \frac{1}{8ba^{3}} times \frac{5b}{5b}. Multiply \frac{1}{10b^{2}} times \frac{4a^{3}}{4a^{3}}.

$$\frac{5b}{40b^{2}a^{3}}+\frac{4a^{3}}{40b^{2}a^{3}}$$

Since \frac{5b}{40b^{2}a^{3}} and \frac{4a^{3}}{40b^{2}a^{3}} have the same denominator, add them by adding their numerators.

$$\frac{5b+4a^{3}}{40b^{2}a^{3}}$$

Factor

$$\frac{\frac{4a^{3}}{b}+5}{40ba^{3}}$$