Algebra Examples

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

Step 1

Simplify the expression.

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Step 1.1

Rewrite using the commutative property of multiplication.

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Cancel the common factor of $4$ .

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Cancel the common factor.

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

Step 2.4

Rewrite the expression.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Multiply $3$ by $2$ .

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

Step 4

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

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Step 4.1

Move $x^{4}$ .

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

Step 4.2

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

$- x^{4 + 6}$

Step 4.3

Add $4$ and $6$ .

$- x^{10}$