Basic Math Examples

$(\frac{2}{3} \cdot (p^{4} y^{3})) (y^{4} s^{5}) (6 p^{2} s^{3})$

Step 1

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

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Step 1.1

Move $p^{2}$ .

$\frac{2}{3} \cdot (p^{2} p^{4} y^{3}) (y^{4} s^{5}) (6 s^{3})$

Step 1.2

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

$\frac{2}{3} \cdot (p^{2 + 4} y^{3}) (y^{4} s^{5}) (6 s^{3})$

Step 1.3

Add $2$ and $4$ .

$\frac{2}{3} \cdot (p^{6} y^{3}) (y^{4} s^{5}) (6 s^{3})$

Step 2

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

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Step 2.1

Move $y^{4}$ .

$\frac{2}{3} \cdot (p^{6} (y^{4} y^{3})) s^{5} (6 s^{3})$

Step 2.2

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

$\frac{2}{3} \cdot (p^{6} y^{4 + 3}) s^{5} (6 s^{3})$

Step 2.3

Add $4$ and $3$ .

$\frac{2}{3} \cdot (p^{6} y^{7}) s^{5} (6 s^{3})$

Step 3

Multiply $s^{5}$ by $s^{3}$ by adding the exponents.

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Step 3.1

Move $s^{3}$ .

$\frac{2}{3} \cdot (p^{6} y^{7}) (s^{3} s^{5}) \cdot 6$

Step 3.2

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

$\frac{2}{3} \cdot (p^{6} y^{7}) s^{3 + 5} \cdot 6$

Step 3.3

Add $3$ and $5$ .

$\frac{2}{3} \cdot (p^{6} y^{7}) s^{8} \cdot 6$

Step 4

Multiply $\frac{2}{3} (p^{6} y^{7})$ .

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Step 4.1

Combine $p^{6}$ and $\frac{2}{3}$ .

$\frac{p^{6} \cdot 2}{3} y^{7} s^{8} \cdot 6$

Step 4.2

Combine $\frac{p^{6} \cdot 2}{3}$ and $y^{7}$ .

$\frac{p^{6} \cdot 2 y^{7}}{3} s^{8} \cdot 6$

Step 5

Move $2$ to the left of $p^{6}$ .

$\frac{2 \cdot p^{6} y^{7}}{3} s^{8} \cdot 6$

Step 6

Combine $\frac{2 p^{6} y^{7}}{3}$ and $s^{8}$ .

$\frac{2 p^{6} y^{7} s^{8}}{3} \cdot 6$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Factor $3$ out of $6$ .

$\frac{2 p^{6} y^{7} s^{8}}{3} \cdot (3 (2))$

Step 7.2

Cancel the common factor.

$\frac{2 p^{6} y^{7} s^{8}}{3} \cdot (3 \cdot 2)$

Step 7.3

Rewrite the expression.

$2 p^{6} y^{7} s^{8} \cdot 2$

Step 8

Multiply $2$ by $2$ .

$4 p^{6} y^{7} s^{8}$