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

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

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

Move $y^{\frac{1}{3}}$ .

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

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

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

Combine the numerators over the common denominator.

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

Subtract $4$ from $1$ .

$3 \cdot 2 y^{\frac{- 3}{3}}$

Divide $- 3$ by $3$ .

$3 \cdot 2 y^{- 1}$

Step 3

Multiply $3$ by $2$ .

$6 y^{- 1}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$6 \frac{1}{y}$

Step 5

Combine $6$ and $\frac{1}{y}$ .

$\frac{6}{y}$