Simplify (3^(1/3)*5^(-1/6))^6

${(3^{\frac{1}{3}} \cdot 5^{- \frac{1}{6}})}^{6}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(3^{\frac{1}{3}} \cdot \frac{1}{5^{\frac{1}{6}}})}^{6}$

Step 2

Combine fractions.

Combine $3^{\frac{1}{3}}$ and $\frac{1}{5^{\frac{1}{6}}}$ .

${(\frac{3^{\frac{1}{3}}}{5^{\frac{1}{6}}})}^{6}$

Apply the product rule to $\frac{3^{\frac{1}{3}}}{5^{\frac{1}{6}}}$ .

$\frac{{(3^{\frac{1}{3}})}^{6}}{{(5^{\frac{1}{6}})}^{6}}$

Step 3

Simplify the numerator.

Multiply the exponents in ${(3^{\frac{1}{3}})}^{6}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{3^{\frac{1}{3} \cdot 6}}{{(5^{\frac{1}{6}})}^{6}}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{3^{\frac{1}{3} \cdot (3 (2))}}{{(5^{\frac{1}{6}})}^{6}}$

Cancel the common factor.

$\frac{3^{\frac{1}{3} \cdot (3 \cdot 2)}}{{(5^{\frac{1}{6}})}^{6}}$

Rewrite the expression.

$\frac{3^{2}}{{(5^{\frac{1}{6}})}^{6}}$

Raise $3$ to the power of $2$ .

$\frac{9}{{(5^{\frac{1}{6}})}^{6}}$

Step 4

Simplify the denominator.

Multiply the exponents in ${(5^{\frac{1}{6}})}^{6}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{9}{5^{\frac{1}{6} \cdot 6}}$

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{9}{5^{\frac{1}{6} \cdot 6}}$

Rewrite the expression.

$\frac{9}{5^{1}}$

Evaluate the exponent.

$\frac{9}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{5}$

Decimal Form:

$1.8$

Mixed Number Form:

$1 \frac{4}{5}$