Simplify (27^(-2/3))/(27^(-1/3))

$\frac{27^{- \frac{2}{3}}}{27^{- \frac{1}{3}}}$

Step 1

Move $27^{- \frac{2}{3}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{27^{- \frac{1}{3}} \cdot 27^{\frac{2}{3}}}$

Step 2

Multiply $27^{- \frac{1}{3}}$ by $27^{\frac{2}{3}}$ by adding the exponents.

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

$\frac{1}{27^{- \frac{1}{3} + \frac{2}{3}}}$

Combine the numerators over the common denominator.

$\frac{1}{27^{\frac{- 1 + 2}{3}}}$

Add $- 1$ and $2$ .

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

Step 3

Simplify the denominator.

Rewrite $27$ as $3^{3}$ .

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$