simplify 1/9^(1/3) — step-by-step solution

Let's reduce:

\frac{1}{9^{\frac{1}{3}}}

Multiply numerator and denominator by

3^{\frac{1}{3}}

so that the number under the root becomes an exact power:

9 \times 3

27

3^{3}

ⅰ

\frac{1}{9^{\frac{1}{3}}}

\frac{3^{\frac{1}{3}}}{27^{\frac{1}{3}}}

\frac{3^{\frac{1}{3}}}{27^{\frac{1}{3}}}

ⓘ The root of order

3

is the number whose power

3

equals the radicand:

27^{\frac{1}{3}}

3

;

3^{3}

27

▶Simplified form:

\frac{3^{\frac{1}{3}}}{3}

The numeric value of:

\frac{3^{\frac{1}{3}}}{3}

equals:

\frac{\approx 1.4422}{3}

▷

\approx 0.4807