Solve x^3(1/x^-10+4x^2/x^5)

$${ x }^{ 3 } ( \frac{ 1 }{ { x }^{ -10 } } + \frac{ 4 { x }^{ 2 } }{ { x }^{ 5 } } )$$

Evaluate

$$x^{13}+4$$

Solution Steps

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

$$x^{3}\left(\frac{1}{x^{-10}}+\frac{4}{x^{3}}\right)$$

Use the distributive property to multiply x^{3} by \frac{1}{x^{-10}}+\frac{4}{x^{3}}.

$$x^{3}\times \frac{1}{x^{-10}}+x^{3}\times \frac{4}{x^{3}}$$

Express x^{3}\times \frac{1}{x^{-10}} as a single fraction.

$$\frac{x^{3}}{x^{-10}}+x^{3}\times \frac{4}{x^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$x^{13}+x^{3}\times \frac{4}{x^{3}}$$

Cancel out x^{3} and x^{3}.

$$x^{13}+4$$

Expand

$$x^{13}+4$$

Solution Steps

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

$$x^{3}\left(\frac{1}{x^{-10}}+\frac{4}{x^{3}}\right)$$

Use the distributive property to multiply x^{3} by \frac{1}{x^{-10}}+\frac{4}{x^{3}}.

$$x^{3}\times \frac{1}{x^{-10}}+x^{3}\times \frac{4}{x^{3}}$$

Express x^{3}\times \frac{1}{x^{-10}} as a single fraction.

$$\frac{x^{3}}{x^{-10}}+x^{3}\times \frac{4}{x^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$x^{13}+x^{3}\times \frac{4}{x^{3}}$$

Cancel out x^{3} and x^{3}.

$$x^{13}+4$$