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

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

Step 1

Simplify the expression.

Rewrite using the commutative property of multiplication.

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

Apply the product rule to $- 2 x^{3}$ .

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

Raise $- 2$ to the power of $2$ .

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

Step 2

Cancel the common factor of $4$ .

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

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

Factor $4$ out of $4 {(x^{3})}^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- {(x^{3})}^{2} x^{4}$

Step 3

Multiply the exponents in ${(x^{3})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Multiply $3$ by $2$ .

$- x^{6} x^{4}$

Step 4

Multiply $x^{6}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$- (x^{4} x^{6})$

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

$- x^{4 + 6}$

Add $4$ and $6$ .

$- x^{10}$