Basic Math Examples

$\frac{12 m a r b l e \cdot 1}{2} \cdot \frac{r e d \cdot 1}{4} \cdot \frac{b l u e \cdot 1}{4} \cdot (g r e e n)$

Step 1

Rewrite using the commutative property of multiplication.

$e e \frac{12 m a r b l e}{2} \frac{r e d}{4} \frac{b l u e}{4} (g r n)$

Step 2

Multiply $e e$ .

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Step 2.1

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

$e^{1} e \frac{12 m a r b l e}{2} \frac{r e d}{4} \frac{b l u e}{4} (g r n)$

Step 2.2

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

$e^{1} e^{1} \frac{12 m a r b l e}{2} \frac{r e d}{4} \frac{b l u e}{4} (g r n)$

Step 2.3

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

$e^{1 + 1} \frac{12 m a r b l e}{2} \frac{r e d}{4} \frac{b l u e}{4} (g r n)$

Step 2.4

Add $1$ and $1$ .

$e^{2} \frac{12 m a r b l e}{2} \frac{r e d}{4} \frac{b l u e}{4} (g r n)$

Step 3

Cancel the common factor of $12$ and $2$ .

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Step 3.1

Factor $2$ out of $12 m a r b l e$ .

$e^{2} \frac{2 (6 m a r b l e)}{2} \frac{r e d}{4} \frac{b l u e}{4} (g r n)$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $2$ .

$e^{2} \frac{2 (6 m a r b l e)}{2 (1)} \frac{r e d}{4} \frac{b l u e}{4} (g r n)$

Step 3.2.2

Cancel the common factor.

$e^{2} \frac{2 (6 m a r b l e)}{2 \cdot 1} \frac{r e d}{4} \frac{b l u e}{4} (g r n)$

Step 3.2.3

Rewrite the expression.

$e^{2} \frac{6 m a r b l e}{1} \frac{r e d}{4} \frac{b l u e}{4} (g r n)$

Step 3.2.4

Divide $6 m a r b l e$ by $1$ .

$e^{2} (6 m a r b l e) \frac{r e d}{4} \frac{b l u e}{4} (g r n)$

Step 4

Multiply $e^{2}$ by $e$ by adding the exponents.

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Step 4.1

Move $e$ .

$e e^{2} (6 m a r b l) \frac{r e d}{4} \frac{b l u e}{4} (g r n)$

Step 4.2

Multiply $e$ by $e^{2}$ .

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Step 4.2.1

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

$e^{1} e^{2} (6 m a r b l) \frac{r e d}{4} \frac{b l u e}{4} (g r n)$

Step 4.2.2

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

$e^{1 + 2} (6 m a r b l) \frac{r e d}{4} \frac{b l u e}{4} (g r n)$

Step 4.3

Add $1$ and $2$ .

$e^{3} (6 m a r b l) \frac{r e d}{4} \frac{b l u e}{4} (g r n)$

Step 5

Multiply $r$ by $r$ by adding the exponents.

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Step 5.1

Move $r$ .

$e^{3} (6 m a (r \cdot r) b l) \frac{r e d}{4} \frac{b l u e}{4} (g n)$

Step 5.2

Multiply $r$ by $r$ .

$e^{3} (6 m a r^{2} b l) \frac{r e d}{4} \frac{b l u e}{4} (g n)$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $e^{3} (6 m a r^{2} b l) \frac{r e d}{4}$ .

$2 (e^{3} (3 m a r^{2} b l) \frac{r e d}{4}) \frac{b l u e}{4} (g n)$

Step 6.2

Factor $2$ out of $4$ .

$2 (e^{3} (3 m a r^{2} b l) \frac{r e d}{4}) \frac{b l u e}{2 (2)} (g n)$

Step 6.3

Cancel the common factor.

$2 (e^{3} (3 m a r^{2} b l) \frac{r e d}{4}) \frac{b l u e}{2 \cdot 2} (g n)$

Step 6.4

Rewrite the expression.

$e^{3} (3 m a r^{2} b l) \frac{r e d}{4} \frac{b l u e}{2} (g n)$

Step 7

Combine $e^{3}$ and $\frac{r e d}{4}$ .

$3 m a r^{2} b l \frac{e^{3} (r e d)}{4} \frac{b l u e}{2} (g n)$

Step 8

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

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Step 8.1

Move $e$ .

$3 m a r^{2} b l \frac{e e^{3} (r d)}{4} \frac{b l u e}{2} (g n)$

Step 8.2

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

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Step 8.2.1

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

$3 m a r^{2} b l \frac{e^{1} e^{3} (r d)}{4} \frac{b l u e}{2} (g n)$

Step 8.2.2

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

$3 m a r^{2} b l \frac{e^{1 + 3} (r d)}{4} \frac{b l u e}{2} (g n)$

Step 8.3

Add $1$ and $3$ .

$3 m a r^{2} b l \frac{e^{4} (r d)}{4} \frac{b l u e}{2} (g n)$

Step 9

Combine $3$ and $\frac{e^{4} (r d)}{4}$ .

$m a r^{2} b l \frac{3 (e^{4} (r d))}{4} \frac{b l u e}{2} (g n)$

Step 10

Combine $m$ and $\frac{3 (e^{4} (r d))}{4}$ .

$a r^{2} b l \frac{m (3 (e^{4} (r d)))}{4} \frac{b l u e}{2} (g n)$

Step 11

Combine $a$ and $\frac{m (3 (e^{4} (r d)))}{4}$ .

$r^{2} b l \frac{a (m (3 (e^{4} (r d))))}{4} \frac{b l u e}{2} (g n)$

Step 12

Combine $r^{2}$ and $\frac{a (m (3 (e^{4} (r d))))}{4}$ .

$b l \frac{r^{2} (a (m (3 (e^{4} (r d)))))}{4} \frac{b l u e}{2} (g n)$

Step 13

Multiply $r^{2}$ by $r$ by adding the exponents.

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Step 13.1

Move $r$ .

$b l \frac{r \cdot r^{2} (a (m (3 (e^{4} (d)))))}{4} \frac{b l u e}{2} (g n)$

Step 13.2

Multiply $r$ by $r^{2}$ .

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Step 13.2.1

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

$b l \frac{r^{1} r^{2} (a (m (3 (e^{4} (d)))))}{4} \frac{b l u e}{2} (g n)$

Step 13.2.2

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

$b l \frac{r^{1 + 2} (a (m (3 (e^{4} (d)))))}{4} \frac{b l u e}{2} (g n)$

Step 13.3

Add $1$ and $2$ .

$b l \frac{r^{3} (a (m (3 (e^{4} (d)))))}{4} \frac{b l u e}{2} (g n)$

Step 14

Combine $b$ and $\frac{r^{3} (a (m (3 (e^{4} (d)))))}{4}$ .

$l \frac{b (r^{3} (a (m (3 (e^{4} (d))))))}{4} \frac{b l u e}{2} (g n)$

Step 15

Combine $l$ and $\frac{b (r^{3} (a (m (3 (e^{4} (d))))))}{4}$ .

$\frac{l (b (r^{3} (a (m (3 (e^{4} (d)))))))}{4} \cdot \frac{b l u e}{2} (g n)$

Step 16

Multiply $\frac{l (b (r^{3} (a (m (3 (e^{4} (d)))))))}{4}$ by $\frac{b l u e}{2}$ .

$\frac{l (b (r^{3} (a (m (3 (e^{4} (d))))))) (b l u e)}{4 \cdot 2} (g n)$

Step 17

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

$\frac{b (r^{3} (a (m (3 (e^{4} (d)))))) (b (l^{1} l) u e)}{4 \cdot 2} (g n)$

Step 18

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

$\frac{b (r^{3} (a (m (3 (e^{4} (d)))))) (b (l^{1} l^{1}) u e)}{4 \cdot 2} (g n)$

Step 19

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

$\frac{b (r^{3} (a (m (3 (e^{4} (d)))))) (b l^{1 + 1} u e)}{4 \cdot 2} (g n)$

Step 20

Add $1$ and $1$ .

$\frac{b (r^{3} (a (m (3 (e^{4} (d)))))) (b l^{2} u e)}{4 \cdot 2} (g n)$

Step 21

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

$\frac{b^{1} b (r^{3} (a (m (3 (e^{4} (d)))))) (l^{2} u e)}{4 \cdot 2} (g n)$

Step 22

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

$\frac{b^{1} b^{1} (r^{3} (a (m (3 (e^{4} (d)))))) (l^{2} u e)}{4 \cdot 2} (g n)$

Step 23

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

$\frac{b^{1 + 1} (r^{3} (a (m (3 (e^{4} (d)))))) (l^{2} u e)}{4 \cdot 2} (g n)$

Step 24

Add $1$ and $1$ .

$\frac{b^{2} (r^{3} (a (m (3 (e^{4} (d)))))) (l^{2} u e)}{4 \cdot 2} (g n)$

Step 25

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

$\frac{b^{2} (r^{3} (a (m (3 (d))))) (l^{2} u (e^{4} e^{1}))}{4 \cdot 2} (g n)$

Step 26

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

$\frac{b^{2} (r^{3} (a (m (3 (d))))) (l^{2} u e^{4 + 1})}{4 \cdot 2} (g n)$

Step 27

Add $4$ and $1$ .

$\frac{b^{2} (r^{3} (a (m (3 (d))))) (l^{2} u e^{5})}{4 \cdot 2} (g n)$

Step 28

Multiply $4$ by $2$ .

$\frac{b^{2} (r^{3} (a (m (3 (d))))) (l^{2} u e^{5})}{8} (g n)$

Step 29

Move $3$ to the left of $b^{2} r^{3} a m$ .

$\frac{3 \cdot (b^{2} r^{3} a m) d l^{2} u e^{5}}{8} (g n)$

Step 30

Multiply $\frac{3 b^{2} r^{3} a m d l^{2} u e^{5}}{8} (g n)$ .

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Step 30.1

Combine $g$ and $\frac{3 b^{2} r^{3} a m d l^{2} u e^{5}}{8}$ .

$\frac{g (3 b^{2} r^{3} a m d l^{2} u e^{5})}{8} n$

Step 30.2

Combine $\frac{g (3 b^{2} r^{3} a m d l^{2} u e^{5})}{8}$ and $n$ .

$\frac{g (3 b^{2} r^{3} a m d l^{2} u e^{5}) n}{8}$

Step 31

Move $3$ to the left of $g$ .

$\frac{3 g b^{2} r^{3} a m d l^{2} u e^{5} n}{8}$