Simplify (27^(4/3))/(27^(2/3))

$\frac{27^{\frac{4}{3}}}{27^{\frac{2}{3}}}$

Step 1

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

$27^{\frac{4}{3}} \cdot 27^{- \frac{2}{3}}$

Step 2

Multiply $27^{\frac{4}{3}}$ by $27^{- \frac{2}{3}}$ by adding the exponents.

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

$27^{\frac{4}{3} - \frac{2}{3}}$

Combine the numerators over the common denominator.

$27^{\frac{4 - 2}{3}}$

Subtract $2$ from $4$ .

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

Step 3

Simplify the expression.

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

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

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

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

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$3^{2}$

Step 5

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

$9$