Simplify the Radical Expression 3^(1/4)*27^(1/4)

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

Step 1

Multiply $3^{\frac{1}{4}} \cdot 27^{\frac{1}{4}}$ .

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

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

Multiply the exponents in ${(3^{3})}^{\frac{1}{4}}$ .

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

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

Combine $3$ and $\frac{1}{4}$ .

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

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

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

Combine the numerators over the common denominator.

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

Add $1$ and $3$ .

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$3^{1}$

Step 2

Evaluate the exponent.

$3$