Algebra Examples

${(\frac{9^{3}}{6^{3}})}^{- \frac{1}{3}}$

Step 1

Evaluate the exponents.

Tap for more steps...

Step 1.1

Raise $9$ to the power of $3$ .

${(\frac{729}{6^{3}})}^{- \frac{1}{3}}$

Step 1.2

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

${(\frac{729}{216})}^{- \frac{1}{3}}$

Step 2

Cancel the common factor of $729$ and $216$ .

Tap for more steps...

Step 2.1

Factor $27$ out of $729$ .

${(\frac{27 (27)}{216})}^{- \frac{1}{3}}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $27$ out of $216$ .

${(\frac{27 \cdot 27}{27 \cdot 8})}^{- \frac{1}{3}}$

Step 2.2.2

Cancel the common factor.

${(\frac{27 \cdot 27}{27 \cdot 8})}^{- \frac{1}{3}}$

Step 2.2.3

Rewrite the expression.

${(\frac{27}{8})}^{- \frac{1}{3}}$

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{8}{27})}^{\frac{1}{3}}$

Step 4

Apply the product rule to $\frac{8}{27}$ .

$\frac{8^{\frac{1}{3}}}{27^{\frac{1}{3}}}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Rewrite $8$ as $2^{3}$ .

$\frac{{(2^{3})}^{\frac{1}{3}}}{27^{\frac{1}{3}}}$

Step 5.2

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

$\frac{2^{3 (\frac{1}{3})}}{27^{\frac{1}{3}}}$

Step 5.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 5.3.1

Cancel the common factor.

$\frac{2^{3 (\frac{1}{3})}}{27^{\frac{1}{3}}}$

Step 5.3.2

Rewrite the expression.

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

Step 5.4

Evaluate the exponent.

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

Step 6

Simplify the denominator.

Tap for more steps...

Step 6.1

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

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

Step 6.2

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

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

Step 6.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.3.1

Cancel the common factor.

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

Step 6.3.2

Rewrite the expression.

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

Step 6.4

Evaluate the exponent.

$\frac{2}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$