Simplify (6^(1/3))÷(6^(10/3))

$6^{\frac{1}{3}} \div 6^{\frac{10}{3}}$

Rewrite the division as a fraction.

$\frac{6^{\frac{1}{3}}}{6^{\frac{10}{3}}}$

Move $6^{\frac{1}{3}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{1}{6^{\frac{10}{3}} \cdot 6^{- \frac{1}{3}}}$

Multiply $6^{\frac{10}{3}}$ by $6^{- \frac{1}{3}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{6^{\frac{10}{3} - \frac{1}{3}}}$

Combine the numerators over the common denominator.

$\frac{1}{6^{\frac{10 - 1}{3}}}$

Subtract $1$ from $10$ .

$\frac{1}{6^{\frac{9}{3}}}$

Divide $9$ by $3$ .

$\frac{1}{6^{3}}$

Raise $6$ to the power of $3$ .

$\frac{1}{216}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{216}$

Decimal Form:

$0.004\overline{629}$