Question

Simplify the expression. $$\frac{13 x^{4}}{7 x} \div \frac{x^{3}}{7 x}$$

Short answer

The simplified form of the given expression is \(13x.\)

Step-by-step solution

Rewrite the Division as Multiplication

Division of fractions is equivalent to multiplying by the reciprocal of the divisor. So, the given expression can be rewritten as \(\frac{13 x^{4}}{7 x} \times \frac{7 x}{x^{3}}.\)

Cancel out common factors in the numerator and denominator

In the resulting expression, '7x' appears in both the numerator and the denominator, they can be canceled out, resulting in the simplification to \(13x^{4 - 1} \times 1/{x^{3 - 1}}.\)

Simplify the Exponents

Following the law of exponents such that \(a^{m-n}=a^{m}/a^{n}\) where 'm' and 'n' are any integers and 'a' is any real number, simplify the expression to \(13x^3 \times 1/x^2.\)

Perform Final Simplification

Simplifying further gives the final answer, \(13x.\)