Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$4^{- 1} y^{3} x^{3} m^{- 2} + 2 x^{5} \cdot 4$

Step 2.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2.3

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

$\frac{y^{3}}{4} x^{3} m^{- 2} + 2 x^{5} \cdot 4$

Step 2.4

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

$\frac{y^{3} x^{3}}{4} m^{- 2} + 2 x^{5} \cdot 4$

Step 2.5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{y^{3} x^{3}}{4} \cdot \frac{1}{m^{2}} + 2 x^{5} \cdot 4$

Step 2.6

Combine.

$\frac{y^{3} x^{3} \cdot 1}{4 m^{2}} + 2 x^{5} \cdot 4$

Step 2.7

Multiply $y^{3}$ by $1$ .

$\frac{x^{3} \cdot y^{3}}{4 m^{2}} + 2 x^{5} \cdot 4$

Step 2.8

Multiply $4$ by $2$ .

$\frac{x^{3} y^{3}}{4 m^{2}} + 8 x^{5}$