Simplify (3^(1/3)*27^(2/3))/(8^(4/3))

$\frac{3^{\frac{1}{3}} \cdot 27^{\frac{2}{3}}}{8^{\frac{4}{3}}}$

Step 1

Simplify the numerator.

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

$\frac{3^{\frac{1}{3}} \cdot {(3^{3})}^{\frac{2}{3}}}{8^{\frac{4}{3}}}$

Multiply the exponents in ${(3^{3})}^{\frac{2}{3}}$ .

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

$\frac{3^{\frac{1}{3}} \cdot 3^{3 (\frac{2}{3})}}{8^{\frac{4}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3^{\frac{1}{3}} \cdot 3^{3 (\frac{2}{3})}}{8^{\frac{4}{3}}}$

Rewrite the expression.

$\frac{3^{\frac{1}{3}} \cdot 3^{2}}{8^{\frac{4}{3}}}$

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

$\frac{3^{\frac{1}{3} + 2}}{8^{\frac{4}{3}}}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3^{\frac{1}{3} + 2 \cdot \frac{3}{3}}}{8^{\frac{4}{3}}}$

Combine $2$ and $\frac{3}{3}$ .

$\frac{3^{\frac{1}{3} + \frac{2 \cdot 3}{3}}}{8^{\frac{4}{3}}}$

Combine the numerators over the common denominator.

$\frac{3^{\frac{1 + 2 \cdot 3}{3}}}{8^{\frac{4}{3}}}$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{3^{\frac{1 + 6}{3}}}{8^{\frac{4}{3}}}$

Add $1$ and $6$ .

$\frac{3^{\frac{7}{3}}}{8^{\frac{4}{3}}}$

Step 2

Simplify the denominator.

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

$\frac{3^{\frac{7}{3}}}{{(2^{3})}^{\frac{4}{3}}}$

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

$\frac{3^{\frac{7}{3}}}{2^{3 (\frac{4}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3^{\frac{7}{3}}}{2^{3 (\frac{4}{3})}}$

Rewrite the expression.

$\frac{3^{\frac{7}{3}}}{2^{4}}$

Raise $2$ to the power of $4$ .

$\frac{3^{\frac{7}{3}}}{16}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{3^{\frac{7}{3}}}{16}$

Decimal Form:

$0.81126538 \dots$