Simplify (-4/3xy^3)*(9x^8y)

$(- \frac{4}{3} x y^{3}) \cdot (9 x^{8} y)$

Multiply $x$ by $x^{8}$ by adding the exponents.

Move $x^{8}$ .

$- \frac{4}{3} \cdot (x^{8} x y^{3}) \cdot (9 y)$

Multiply $x^{8}$ by $x$ .

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

$- \frac{4}{3} \cdot (x^{8} x^{1} y^{3}) \cdot (9 y)$

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

$- \frac{4}{3} \cdot (x^{8 + 1} y^{3}) \cdot (9 y)$

Add $8$ and $1$ .

$- \frac{4}{3} \cdot (x^{9} y^{3}) \cdot (9 y)$

Multiply $y^{3}$ by $y$ by adding the exponents.

Move $y$ .

$- \frac{4}{3} \cdot (x^{9} (y \cdot y^{3})) \cdot 9$

Multiply $y$ by $y^{3}$ .

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

$- \frac{4}{3} \cdot (x^{9} (y^{1} y^{3})) \cdot 9$

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

$- \frac{4}{3} \cdot (x^{9} y^{1 + 3}) \cdot 9$

Add $1$ and $3$ .

$- \frac{4}{3} \cdot (x^{9} y^{4}) \cdot 9$

Multiply $- \frac{4}{3} (x^{9} y^{4})$ .

Combine $x^{9}$ and $\frac{4}{3}$ .

$- \frac{x^{9} \cdot 4}{3} y^{4} \cdot 9$

Combine $y^{4}$ and $\frac{x^{9} \cdot 4}{3}$ .

$- \frac{y^{4} (x^{9} \cdot 4)}{3} \cdot 9$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{y^{4} x^{9} \cdot 4}{3}$ into the numerator.

$\frac{- y^{4} x^{9} \cdot 4}{3} \cdot 9$

Factor $3$ out of $9$ .

$\frac{- y^{4} x^{9} \cdot 4}{3} \cdot (3 (3))$

Cancel the common factor.

$\frac{- y^{4} x^{9} \cdot 4}{3} \cdot (3 \cdot 3)$

Rewrite the expression.

$- y^{4} x^{9} \cdot 4 \cdot 3$

Multiply.

Multiply $4$ by $- 1$ .

$- 4 y^{4} x^{9} \cdot 3$

Multiply $3$ by $- 4$ .

$- 12 y^{4} x^{9}$