Simplify 2x^(3/4)*4x^(-1/4)

$2 x^{\frac{3}{4}} \cdot 4 x^{- \frac{1}{4}}$

Step 1

Rewrite using the commutative property of multiplication.

$2 \cdot 4 x^{\frac{3}{4}} x^{- \frac{1}{4}}$

Step 2

Multiply $x^{\frac{3}{4}}$ by $x^{- \frac{1}{4}}$ by adding the exponents.

Move $x^{- \frac{1}{4}}$ .

$2 \cdot 4 (x^{- \frac{1}{4}} x^{\frac{3}{4}})$

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

$2 \cdot 4 x^{- \frac{1}{4} + \frac{3}{4}}$

Combine the numerators over the common denominator.

$2 \cdot 4 x^{\frac{- 1 + 3}{4}}$

Add $- 1$ and $3$ .

$2 \cdot 4 x^{\frac{2}{4}}$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$2 \cdot 4 x^{\frac{2 (1)}{4}}$

Cancel the common factors.

Factor $2$ out of $4$ .

$2 \cdot 4 x^{\frac{2 \cdot 1}{2 \cdot 2}}$

Cancel the common factor.

$2 \cdot 4 x^{\frac{2 \cdot 1}{2 \cdot 2}}$

Rewrite the expression.

$2 \cdot 4 x^{\frac{1}{2}}$

Step 3

Multiply $2$ by $4$ .

$8 x^{\frac{1}{2}}$