Question

simplify the expression. assume that all variables represent positive\\(\frac{4w^{\\ - \frac{1}{7}}}{y^{\\ - \frac{2}{7}}}=\square\\)

Explanation:

Step1: Rewrite negative exponents

A term with a negative exponent in the denominator moves to the numerator with a positive exponent, and vice versa:
$\frac{4w^{-\frac{1}{7}}}{y^{-\frac{2}{7}}} = 4w^{-\frac{1}{7}}y^{\frac{2}{7}}$

Step2: Rewrite positive/negative exponents

A term with a negative exponent can be rewritten as a reciprocal with a positive exponent:
$4w^{-\frac{1}{7}}y^{\frac{2}{7}} = \frac{4y^{\frac{2}{7}}}{w^{\frac{1}{7}}}$

Step3: Convert to radical form (optional, equivalent)

Alternatively, using radical notation for rational exponents:
$\frac{4y^{\frac{2}{7}}}{w^{\frac{1}{7}}} = \frac{4\sqrt[7]{y^2}}{\sqrt[7]{w}}$
Or combine radicals:
$\frac{4\sqrt[7]{y^2}}{\sqrt[7]{w}} = 4\sqrt[7]{\frac{y^2}{w}}$

Answer:

$\frac{4y^{\frac{2}{7}}}{w^{\frac{1}{7}}}$ (or equivalent form $4\sqrt[7]{\frac{y^2}{w}}$)