Algebra Examples

$(\frac{1}{2} x^{3}) (- \frac{2}{3} a^{2} x) (- \frac{3}{5} a^{4} m)$

Step 1

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

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Step 1.1

Move $x$ .

$\frac{1}{2} (x \cdot x^{3}) (- \frac{2}{3} \cdot (a^{2})) (- \frac{3}{5} \cdot (a^{4} m))$

Step 1.2

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

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Step 1.2.1

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

$\frac{1}{2} (x^{1} x^{3}) (- \frac{2}{3} \cdot (a^{2})) (- \frac{3}{5} \cdot (a^{4} m))$

Step 1.2.2

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

$\frac{1}{2} x^{1 + 3} (- \frac{2}{3} \cdot (a^{2})) (- \frac{3}{5} \cdot (a^{4} m))$

Step 1.3

Add $1$ and $3$ .

$\frac{1}{2} x^{4} (- \frac{2}{3} \cdot (a^{2})) (- \frac{3}{5} \cdot (a^{4} m))$

Step 2

Multiply $a^{2}$ by $a^{4}$ by adding the exponents.

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Step 2.1

Move $a^{4}$ .

$\frac{1}{2} x^{4} (- \frac{2}{3} \cdot (a^{4} a^{2})) (- \frac{3}{5} \cdot (m))$

Step 2.2

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

$\frac{1}{2} x^{4} (- \frac{2}{3} \cdot a^{4 + 2}) (- \frac{3}{5} \cdot (m))$

Step 2.3

Add $4$ and $2$ .

$\frac{1}{2} x^{4} (- \frac{2}{3} \cdot a^{6}) (- \frac{3}{5} \cdot (m))$

Step 3

Simplify terms.

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Step 3.1

Rewrite using the commutative property of multiplication.

$\frac{1}{2} \cdot - 1 \frac{2}{3} x^{4} a^{6} (- \frac{3}{5} \cdot (m))$

Step 3.2

Combine $\frac{1}{2}$ and $- 1$ .

$\frac{- 1}{2} \cdot \frac{2}{3} x^{4} a^{6} (- \frac{3}{5} \cdot (m))$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Cancel the common factor.

$\frac{- 1}{2} \cdot \frac{2}{3} x^{4} a^{6} (- \frac{3}{5} \cdot (m))$

Step 3.3.2

Rewrite the expression.

$- \frac{1}{3} x^{4} a^{6} (- \frac{3}{5} \cdot (m))$

Step 3.4

Combine $x^{4}$ and $\frac{1}{3}$ .

$- \frac{x^{4}}{3} a^{6} (- \frac{3}{5} \cdot (m))$

Step 3.5

Combine $a^{6}$ and $\frac{x^{4}}{3}$ .

$- \frac{a^{6} x^{4}}{3} (- \frac{3}{5} \cdot (m))$

Step 3.6

Combine $m$ and $\frac{3}{5}$ .

$- \frac{a^{6} x^{4}}{3} (- \frac{m \cdot 3}{5})$

Step 3.7

Cancel the common factor of $3$ .

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Step 3.7.1

Move the leading negative in $- \frac{a^{6} x^{4}}{3}$ into the numerator.

$\frac{- a^{6} x^{4}}{3} (- \frac{m \cdot 3}{5})$

Step 3.7.2

Move the leading negative in $- \frac{m \cdot 3}{5}$ into the numerator.

$\frac{- a^{6} x^{4}}{3} \cdot \frac{- m \cdot 3}{5}$

Step 3.7.3

Factor $3$ out of $- m \cdot 3$ .

$\frac{- a^{6} x^{4}}{3} \cdot \frac{3 \cdot (- m)}{5}$

Step 3.7.4

Cancel the common factor.

$\frac{- a^{6} x^{4}}{3} \cdot \frac{3 \cdot (- m)}{5}$

Step 3.7.5

Rewrite the expression.

$- a^{6} x^{4} \frac{- m}{5}$

Step 3.8

Combine $a^{6}$ and $\frac{- m}{5}$ .

$- x^{4} \frac{a^{6} (- m)}{5}$

Step 3.9

Combine $\frac{a^{6} (- m)}{5}$ and $x^{4}$ .

$- \frac{a^{6} (- m) x^{4}}{5}$

Step 4

Factor out negative.

$- \frac{- a^{6} m x^{4}}{5}$

Step 5

Move the negative in front of the fraction.

$- - \frac{a^{6} m x^{4}}{5}$

Step 6

Multiply $- - \frac{a^{6} m x^{4}}{5}$ .

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Step 6.1

Multiply $- 1$ by $- 1$ .

$1 \frac{a^{6} m x^{4}}{5}$

Step 6.2

Multiply $\frac{a^{6} m x^{4}}{5}$ by $1$ .

$\frac{a^{6} m x^{4}}{5}$