Simplify (-1/4x^3)(4/9x^4)

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

Multiply $x^{3}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

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

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

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

Add $4$ and $3$ .

$- \frac{1}{4} \cdot \frac{4}{9} x^{7}$

Step 3

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{- 1}{4} \cdot \frac{4}{9} x^{7}$

Cancel the common factor.

$\frac{- 1}{4} \cdot \frac{4}{9} x^{7}$

Rewrite the expression.

$- 1 \cdot \frac{1}{9} x^{7}$

Step 4

Rewrite $- 1 (\frac{1}{9})$ as $- (\frac{1}{9})$ .

$- (\frac{1}{9}) x^{7}$

Step 5

Combine $x^{7}$ and $\frac{1}{9}$ .

$- \frac{x^{7}}{9}$