Simplify (3^(3/4)*27^(3/4))/(9^(3/4))

$\frac{3^{\frac{3}{4}} \cdot 27^{\frac{3}{4}}}{9^{\frac{3}{4}}}$

Step 1

Simplify the numerator.

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

$\frac{3^{\frac{3}{4}} \cdot {(3^{3})}^{\frac{3}{4}}}{9^{\frac{3}{4}}}$

Multiply the exponents in ${(3^{3})}^{\frac{3}{4}}$ .

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

$\frac{3^{\frac{3}{4}} \cdot 3^{3 (\frac{3}{4})}}{9^{\frac{3}{4}}}$

Multiply $3 (\frac{3}{4})$ .

Combine $3$ and $\frac{3}{4}$ .

$\frac{3^{\frac{3}{4}} \cdot 3^{\frac{3 \cdot 3}{4}}}{9^{\frac{3}{4}}}$

Multiply $3$ by $3$ .

$\frac{3^{\frac{3}{4}} \cdot 3^{\frac{9}{4}}}{9^{\frac{3}{4}}}$

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

$\frac{3^{\frac{3}{4} + \frac{9}{4}}}{9^{\frac{3}{4}}}$

Combine the numerators over the common denominator.

$\frac{3^{\frac{3 + 9}{4}}}{9^{\frac{3}{4}}}$

Add $3$ and $9$ .

$\frac{3^{\frac{12}{4}}}{9^{\frac{3}{4}}}$

Cancel the common factor of $12$ and $4$ .

Factor $4$ out of $12$ .

$\frac{3^{\frac{4 \cdot 3}{4}}}{9^{\frac{3}{4}}}$

Cancel the common factors.

Factor $4$ out of $4$ .

$\frac{3^{\frac{4 \cdot 3}{4 (1)}}}{9^{\frac{3}{4}}}$

Cancel the common factor.

$\frac{3^{\frac{4 \cdot 3}{4 \cdot 1}}}{9^{\frac{3}{4}}}$

Rewrite the expression.

$\frac{3^{\frac{3}{1}}}{9^{\frac{3}{4}}}$

Divide $3$ by $1$ .

$\frac{3^{3}}{9^{\frac{3}{4}}}$

Step 2

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

$\frac{27}{9^{\frac{3}{4}}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{27}{9^{\frac{3}{4}}}$

Decimal Form:

$5.19615242 \dots$