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

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

Step 1

Move $27^{\frac{4}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 2

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $3$ .

$27^{\frac{6 - 4}{3}}$

Subtract $4$ from $6$ .

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

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 $2$ .

$9$