Algebra Examples

$m^{2} \cdot 3 m^{4} \cdot 6 a \cdot a^{- 3}$

Step 1

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

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Step 1.1

Move $m^{4}$ .

$m^{4} m^{2} \cdot 3 \cdot (6 a) \cdot a^{- 3}$

Step 1.2

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

$m^{4 + 2} \cdot 3 \cdot (6 a) \cdot a^{- 3}$

Step 1.3

Add $4$ and $2$ .

$m^{6} \cdot 3 \cdot (6 a) \cdot a^{- 3}$

Step 2

Multiply $a$ by $a^{- 3}$ by adding the exponents.

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Step 2.1

Move $a^{- 3}$ .

$m^{6} \cdot 3 \cdot (6 (a^{- 3} a))$

Step 2.2

Multiply $a^{- 3}$ by $a$ .

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Step 2.2.1

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

$m^{6} \cdot 3 \cdot (6 (a^{- 3} a^{1}))$

Step 2.2.2

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

$m^{6} \cdot 3 \cdot (6 a^{- 3 + 1})$

Step 2.3

Add $- 3$ and $1$ .

$m^{6} \cdot 3 \cdot (6 a^{- 2})$

Step 3

Move $3$ to the left of $m^{6}$ .

$3 \cdot m^{6} \cdot (6 a^{- 2})$

Step 4

Rewrite using the commutative property of multiplication.

$3 \cdot 6 m^{6} a^{- 2}$

Step 5

Multiply $3$ by $6$ .

$18 m^{6} a^{- 2}$

Step 6

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

$18 m^{6} \frac{1}{a^{2}}$

Step 7

Multiply $18 m^{6} \frac{1}{a^{2}}$ .

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Step 7.1

Combine $18$ and $\frac{1}{a^{2}}$ .

$m^{6} \frac{18}{a^{2}}$

Step 7.2

Combine $m^{6}$ and $\frac{18}{a^{2}}$ .

$\frac{m^{6} \cdot 18}{a^{2}}$

Step 8

Move $18$ to the left of $m^{6}$ .

$\frac{18 m^{6}}{a^{2}}$