Simplify ((9^3)/(6^3))^(-1/3)

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

Step 1

Evaluate the exponents.

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

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

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

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

Step 2

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

Factor $27$ out of $729$ .

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

Cancel the common factors.

Factor $27$ out of $216$ .

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

Cancel the common factor.

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

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.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 6

Simplify the denominator.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{2}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$

Simplify ((9^3)/(6^3))^(-1/3)

Related Questions

Support LCMGCF.com by disabling your adblocker.