Question

simplifying with fractional exponents

simplify. \\(\frac{x^{\frac{1}{4}} x^{\frac{8}{3}}}{x^2}\\)

\\(x^?\\)

the simplified expression is \\(x\\) to the power of

Explanation:

Combine the numerator exponents

Using the Exponent Rules and Algebraic Simplification knowledge points

$$ x^{\frac{1}{4}} \cdot x^{\frac{8}{3}} = x^{\frac{1}{4} + \frac{8}{3}} = x^{\frac{3}{12} + \frac{32}{12}} = x^{\frac{35}{12}} $$

Divide by the denominator

Using the Exponent Rules and Algebraic Simplification knowledge points

$$ \frac{x^{\frac{35}{12}}}{x^2} = x^{\frac{35}{12} - 2} = x^{\frac{35}{12} - \frac{24}{12}} = x^{\frac{11}{12}} $$

Answer:

The simplified expression is \(x\) to the power of <blank>\(\frac{11}{12}\)</blank>