Solve for x (27^(1/4))/(3^(x/4))=1

$\frac{27^{\frac{1}{4}}}{3^{\frac{x}{4}}} = 1$

Multiply both sides by $3^{\frac{x}{4}}$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $3^{\frac{x}{4}}$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Multiply $3^{\frac{x}{4}}$ by $1$ .

$27^{\frac{1}{4}} = 3^{\frac{x}{4}}$

Solve for $x$ .

Rewrite the equation as $3^{\frac{x}{4}} = 27^{\frac{1}{4}}$ .

$3^{\frac{x}{4}} = 27^{\frac{1}{4}}$

Create equivalent expressions in the equation that all have equal bases.

$3^{\frac{x}{4}} = 3^{3 (\frac{1}{4})}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$\frac{x}{4} = 3 (\frac{1}{4})$

Solve for $x$ .

Multiply both sides of the equation by $4$ .

$4 \frac{x}{4} = 4 (3 (\frac{1}{4}))$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{x}{4} = 4 (3 (\frac{1}{4}))$

Rewrite the expression.

$x = 4 (3 (\frac{1}{4}))$

Simplify the right side.

Simplify $4 (3 (\frac{1}{4}))$ .

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

$x = 4 (\frac{3}{4})$

Cancel the common factor of $4$ .

Cancel the common factor.

$x = 4 (\frac{3}{4})$

Rewrite the expression.

$x = 3$