Pre-Algebra Examples

$\frac{25 p^{9} + 10 p^{7}}{5 p}$

Step 1

Factor $5 p^{7}$ out of $25 p^{9} + 10 p^{7}$ .

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Step 1.1

Factor $5 p^{7}$ out of $25 p^{9}$ .

$\frac{5 p^{7} (5 p^{2}) + 10 p^{7}}{5 p}$

Step 1.2

Factor $5 p^{7}$ out of $10 p^{7}$ .

$\frac{5 p^{7} (5 p^{2}) + 5 p^{7} (2)}{5 p}$

Step 1.3

Factor $5 p^{7}$ out of $5 p^{7} (5 p^{2}) + 5 p^{7} (2)$ .

$\frac{5 p^{7} (5 p^{2} + 2)}{5 p}$

Step 2

Cancel the common factor of $5$ .

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Step 2.1

Cancel the common factor.

$\frac{5 p^{7} (5 p^{2} + 2)}{5 p}$

Step 2.2

Rewrite the expression.

$\frac{p^{7} (5 p^{2} + 2)}{p}$

Step 3

Cancel the common factor of $p^{7}$ and $p$ .

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Step 3.1

Factor $p$ out of $p^{7} (5 p^{2} + 2)$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{p (p^{6} (5 p^{2} + 2))}{p^{1}}$

Step 3.2.2

Factor $p$ out of $p^{1}$ .

$\frac{p (p^{6} (5 p^{2} + 2))}{p \cdot 1}$

Step 3.2.3

Cancel the common factor.

$\frac{p (p^{6} (5 p^{2} + 2))}{p \cdot 1}$

Step 3.2.4

Rewrite the expression.

$\frac{p^{6} (5 p^{2} + 2)}{1}$

Step 3.2.5

Divide $p^{6} (5 p^{2} + 2)$ by $1$ .

$p^{6} (5 p^{2} + 2)$

Step 4

Apply the distributive property.

$p^{6} (5 p^{2}) + p^{6} \cdot 2$

Step 5

Rewrite using the commutative property of multiplication.

$5 p^{6} p^{2} + p^{6} \cdot 2$

Step 6

Move $2$ to the left of $p^{6}$ .

$5 p^{6} p^{2} + 2 \cdot p^{6}$

Step 7

Multiply $p^{6}$ by $p^{2}$ by adding the exponents.

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Step 7.1

Move $p^{2}$ .

$5 (p^{2} p^{6}) + 2 \cdot p^{6}$

Step 7.2

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

$5 p^{2 + 6} + 2 \cdot p^{6}$

Step 7.3

Add $2$ and $6$ .

$5 p^{8} + 2 \cdot p^{6}$

$5 p^{8} + 2 p^{6}$