Pre-Algebra Examples

$(5 a^{4} a^{3} + 2 a^{2}) \div 10 a$

Step 1

Rewrite the division as a fraction.

$\frac{5 a^{4} a^{3} + 2 a^{2}}{10 a}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $a^{4}$ out of $5 a^{4} a^{3} + 2 a^{2}$ .

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Step 2.1.1

Factor $a^{4}$ out of $5 a^{4} a^{3}$ .

$\frac{a^{4} (5 a^{3}) + 2 a^{2}}{10 a}$

Step 2.1.2

Factor $a^{4}$ out of $2 a^{2}$ .

$\frac{a^{4} (5 a^{3}) + a^{4} (2 a^{- 2})}{10 a}$

Step 2.1.3

Factor $a^{4}$ out of $a^{4} (5 a^{3}) + a^{4} (2 a^{- 2})$ .

$\frac{a^{4} (5 a^{3} + 2 a^{- 2})}{10 a}$

Step 2.2

Factor $a^{- 2}$ out of $5 a^{3} + 2 a^{- 2}$ .

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Step 2.2.1

Factor $a^{- 2}$ out of $5 a^{3}$ .

$\frac{a^{4} (a^{- 2} (5 a^{5}) + 2 a^{- 2})}{10 a}$

Step 2.2.2

Factor $a^{- 2}$ out of $2 a^{- 2}$ .

$\frac{a^{4} (a^{- 2} (5 a^{5}) + a^{- 2} \cdot 2)}{10 a}$

Step 2.2.3

Factor $a^{- 2}$ out of $a^{- 2} (5 a^{5}) + a^{- 2} \cdot 2$ .

$\frac{a^{4} (a^{- 2} (5 a^{5} + 2))}{10 a}$

$\frac{a^{4} a^{- 2} (5 a^{5} + 2)}{10 a}$

Step 2.3

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

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Step 2.3.1

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

$\frac{a^{4 - 2} (5 a^{5} + 2)}{10 a}$

Step 2.3.2

Subtract $2$ from $4$ .

$\frac{a^{2} (5 a^{5} + 2)}{10 a}$

Step 3

Cancel the common factor of $a^{2}$ and $a$ .

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Step 3.1

Factor $a$ out of $a^{2} (5 a^{5} + 2)$ .

$\frac{a (a (5 a^{5} + 2))}{10 a}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $a$ out of $10 a$ .

$\frac{a (a (5 a^{5} + 2))}{a \cdot 10}$

Step 3.2.2

Cancel the common factor.

$\frac{a (a (5 a^{5} + 2))}{a \cdot 10}$

Step 3.2.3

Rewrite the expression.

$\frac{a (5 a^{5} + 2)}{10}$

Step 4

Apply the distributive property.

$\frac{a (5 a^{5}) + a \cdot 2}{10}$

Step 5

Rewrite using the commutative property of multiplication.

$\frac{5 a \cdot a^{5} + a \cdot 2}{10}$

Step 6

Move $2$ to the left of $a$ .

$\frac{5 a \cdot a^{5} + 2 \cdot a}{10}$

Step 7

Multiply $a$ by $a^{5}$ by adding the exponents.

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Step 7.1

Move $a^{5}$ .

$\frac{5 (a^{5} a) + 2 \cdot a}{10}$

Step 7.2

Multiply $a^{5}$ by $a$ .

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Step 7.2.1

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

$\frac{5 (a^{5} a^{1}) + 2 \cdot a}{10}$

Step 7.2.2

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

$\frac{5 a^{5 + 1} + 2 \cdot a}{10}$

Step 7.3

Add $5$ and $1$ .

$\frac{5 a^{6} + 2 \cdot a}{10}$

$\frac{5 a^{6} + 2 a}{10}$

Step 8

Split the fraction $\frac{5 a^{6} + 2 a}{10}$ into two fractions.

$\frac{5 a^{6}}{10} + \frac{2 a}{10}$

Step 9

Cancel the common factor of $5$ and $10$ .

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Step 9.1

Factor $5$ out of $5 a^{6}$ .

$\frac{5 (a^{6})}{10} + \frac{2 a}{10}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $5$ out of $10$ .

$\frac{5 a^{6}}{5 \cdot 2} + \frac{2 a}{10}$

Step 9.2.2

Cancel the common factor.

$\frac{5 a^{6}}{5 \cdot 2} + \frac{2 a}{10}$

Step 9.2.3

Rewrite the expression.

$\frac{a^{6}}{2} + \frac{2 a}{10}$

Step 10

Cancel the common factor of $2$ and $10$ .

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Step 10.1

Factor $2$ out of $2 a$ .

$\frac{a^{6}}{2} + \frac{2 (a)}{10}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $2$ out of $10$ .

$\frac{a^{6}}{2} + \frac{2 a}{2 \cdot 5}$

Step 10.2.2

Cancel the common factor.

$\frac{a^{6}}{2} + \frac{2 a}{2 \cdot 5}$

Step 10.2.3

Rewrite the expression.

$\frac{a^{6}}{2} + \frac{a}{5}$