Basic Math Examples

$- 3 q y^{0} \cdot (- 3 q y) \cdot (- 2 q^{- 4})$

Step 1

Multiply $q$ by $q$ by adding the exponents.

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Step 1.1

Move $q$ .

$- 3 (q \cdot q) y^{0} \cdot (- 3 y) \cdot (- 2 q^{- 4})$

Step 1.2

Multiply $q$ by $q$ .

$- 3 q^{2} y^{0} \cdot (- 3 y) \cdot (- 2 q^{- 4})$

Step 2

Simplify $- 3 q^{2} y^{0} \cdot (- 3 y) \cdot (- 2 q^{- 4})$ .

$- 3 q^{2} \cdot (- 3 y) \cdot (- 2 q^{- 4})$

Step 3

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

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Step 3.1

Move $q^{- 4}$ .

$- 3 (q^{- 4} q^{2}) \cdot (- 3 y) \cdot - 2$

Step 3.2

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

$- 3 q^{- 4 + 2} \cdot (- 3 y) \cdot - 2$

Step 3.3

Add $- 4$ and $2$ .

$- 3 q^{- 2} \cdot (- 3 y) \cdot - 2$

Step 4

Rewrite using the commutative property of multiplication.

$- 3 \cdot - 3 q^{- 2} y \cdot - 2$

Step 5

Multiply $- 3$ by $- 3$ .

$9 q^{- 2} y \cdot - 2$

Step 6

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

$9 \frac{1}{q^{2}} y \cdot - 2$

Step 7

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

$\frac{9}{q^{2}} y \cdot - 2$

Step 8

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

$\frac{9 y}{q^{2}} \cdot - 2$

Step 9

Multiply $\frac{9 y}{q^{2}} \cdot - 2$ .

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Step 9.1

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

$\frac{9 y \cdot - 2}{q^{2}}$

Step 9.2

Multiply $- 2$ by $9$ .

$\frac{- 18 y}{q^{2}}$

Step 10

Move the negative in front of the fraction.

$- \frac{18 y}{q^{2}}$