Simplify 2y*3x^-1y^4

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

Step 1

Multiply $y$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

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

Multiply $y^{4}$ by $y$ .

Raise $y$ to the power of $1$ .

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

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

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

Add $4$ and $1$ .

$2 y^{5} \cdot (3 x^{- 1})$

Step 2

Rewrite using the commutative property of multiplication.

$2 \cdot 3 y^{5} x^{- 1}$

Step 3

Multiply $2$ by $3$ .

$6 y^{5} x^{- 1}$

Step 4

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

$6 y^{5} \frac{1}{x}$

Step 5

Multiply $6 y^{5} \frac{1}{x}$ .

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

$y^{5} \frac{6}{x}$

Combine $y^{5}$ and $\frac{6}{x}$ .

$\frac{y^{5} \cdot 6}{x}$

Step 6

Move $6$ to the left of $y^{5}$ .

$\frac{6 y^{5}}{x}$