Algebra Examples

$3 a \div a^{- 2} + a^{2} \cdot a - \frac{6 a^{- 1}}{2 a^{- 4}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$\frac{3 a}{a^{- 2}} + a^{2} \cdot a - \frac{6 a^{- 1}}{2 a^{- 4}}$

Step 1.2

Move $a^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$3 a \cdot a^{2} + a^{2} \cdot a - \frac{6 a^{- 1}}{2 a^{- 4}}$

Step 1.3

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

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Step 1.3.1

Move $a^{2}$ .

$3 (a^{2} a) + a^{2} \cdot a - \frac{6 a^{- 1}}{2 a^{- 4}}$

Step 1.3.2

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

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Step 1.3.2.1

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

$3 (a^{2} a^{1}) + a^{2} \cdot a - \frac{6 a^{- 1}}{2 a^{- 4}}$

Step 1.3.2.2

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

$3 a^{2 + 1} + a^{2} \cdot a - \frac{6 a^{- 1}}{2 a^{- 4}}$

Step 1.3.3

Add $2$ and $1$ .

$3 a^{3} + a^{2} \cdot a - \frac{6 a^{- 1}}{2 a^{- 4}}$

Step 1.4

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

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Step 1.4.1

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

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Step 1.4.1.1

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

$3 a^{3} + a^{2} \cdot a^{1} - \frac{6 a^{- 1}}{2 a^{- 4}}$

Step 1.4.1.2

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

$3 a^{3} + a^{2 + 1} - \frac{6 a^{- 1}}{2 a^{- 4}}$

Step 1.4.2

Add $2$ and $1$ .

$3 a^{3} + a^{3} - \frac{6 a^{- 1}}{2 a^{- 4}}$

Step 1.5

Move $a^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$3 a^{3} + a^{3} - \frac{6 a^{- 1} a^{4}}{2}$

Step 1.6

Multiply $a^{- 1}$ by $a^{4}$ by adding the exponents.

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Step 1.6.1

Move $a^{4}$ .

$3 a^{3} + a^{3} - \frac{6 (a^{4} a^{- 1})}{2}$

Step 1.6.2

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

$3 a^{3} + a^{3} - \frac{6 a^{4 - 1}}{2}$

Step 1.6.3

Subtract $1$ from $4$ .

$3 a^{3} + a^{3} - \frac{6 a^{3}}{2}$

Step 1.7

Cancel the common factor of $6$ and $2$ .

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Step 1.7.1

Factor $2$ out of $6 a^{3}$ .

$3 a^{3} + a^{3} - \frac{2 (3 a^{3})}{2}$

Step 1.7.2

Cancel the common factors.

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Step 1.7.2.1

Factor $2$ out of $2$ .

$3 a^{3} + a^{3} - \frac{2 (3 a^{3})}{2 (1)}$

Step 1.7.2.2

Cancel the common factor.

$3 a^{3} + a^{3} - \frac{2 (3 a^{3})}{2 \cdot 1}$

Step 1.7.2.3

Rewrite the expression.

$3 a^{3} + a^{3} - \frac{3 a^{3}}{1}$

Step 1.7.2.4

Divide $3 a^{3}$ by $1$ .

$3 a^{3} + a^{3} - (3 a^{3})$

Step 1.8

Multiply $3$ by $- 1$ .

$3 a^{3} + a^{3} - 3 a^{3}$

Step 2

Combine the opposite terms in $3 a^{3} + a^{3} - 3 a^{3}$ .

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Step 2.1

Subtract $3 a^{3}$ from $3 a^{3}$ .

$a^{3} + 0$

Step 2.2

Add $a^{3}$ and $0$ .

$a^{3}$