Basic Math Examples

$3 y^{3} \cdot (12 z^{5}) \cdot 2^{- 3}$

Step 1

Rewrite using the commutative property of multiplication.

$3 \cdot 12 y^{3} z^{5} \cdot 2^{- 3}$

Step 2

Multiply $3$ by $12$ .

$36 y^{3} z^{5} \cdot 2^{- 3}$

Step 3

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

$36 y^{3} z^{5} \cdot \frac{1}{2^{3}}$

Step 4

Raise $2$ to the power of $3$ .

$36 y^{3} z^{5} \cdot \frac{1}{8}$

Step 5

Cancel the common factor of $4$ .

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Step 5.1

Factor $4$ out of $36 y^{3} z^{5}$ .

$4 (9 y^{3} z^{5}) \cdot \frac{1}{8}$

Step 5.2

Factor $4$ out of $8$ .

$4 (9 y^{3} z^{5}) \cdot \frac{1}{4 (2)}$

Step 5.3

Cancel the common factor.

$4 (9 y^{3} z^{5}) \cdot \frac{1}{4 \cdot 2}$

Step 5.4

Rewrite the expression.

$9 y^{3} z^{5} \cdot \frac{1}{2}$

Step 6

Combine $9$ and $\frac{1}{2}$ .

$y^{3} z^{5} \cdot \frac{9}{2}$

Step 7

Combine $y^{3}$ and $\frac{9}{2}$ .

$z^{5} \cdot \frac{y^{3} \cdot 9}{2}$

Step 8

Combine $z^{5}$ and $\frac{y^{3} \cdot 9}{2}$ .

$\frac{z^{5} (y^{3} \cdot 9)}{2}$

Step 9

Move $9$ to the left of $z^{5} y^{3}$ .

$\frac{9 z^{5} y^{3}}{2}$