Algebra Examples

$(\frac{6}{7} p^{4} r^{3}) (r^{2} z^{4}) (14 p^{3} z^{2})$

Step 1

Multiply $p^{4}$ by $p^{3}$ by adding the exponents.

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Step 1.1

Move $p^{3}$ .

$\frac{6}{7} \cdot (p^{3} p^{4} r^{3}) (r^{2} z^{4}) (14 z^{2})$

Step 1.2

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

$\frac{6}{7} \cdot (p^{3 + 4} r^{3}) (r^{2} z^{4}) (14 z^{2})$

Step 1.3

Add $3$ and $4$ .

$\frac{6}{7} \cdot (p^{7} r^{3}) (r^{2} z^{4}) (14 z^{2})$

Step 2

Multiply $r^{3}$ by $r^{2}$ by adding the exponents.

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Step 2.1

Move $r^{2}$ .

$\frac{6}{7} \cdot (p^{7} (r^{2} r^{3})) z^{4} (14 z^{2})$

Step 2.2

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

$\frac{6}{7} \cdot (p^{7} r^{2 + 3}) z^{4} (14 z^{2})$

Step 2.3

Add $2$ and $3$ .

$\frac{6}{7} \cdot (p^{7} r^{5}) z^{4} (14 z^{2})$

Step 3

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

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Step 3.1

Move $z^{2}$ .

$\frac{6}{7} \cdot (p^{7} r^{5}) (z^{2} z^{4}) \cdot 14$

Step 3.2

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

$\frac{6}{7} \cdot (p^{7} r^{5}) z^{2 + 4} \cdot 14$

Step 3.3

Add $2$ and $4$ .

$\frac{6}{7} \cdot (p^{7} r^{5}) z^{6} \cdot 14$

Step 4

Multiply $\frac{6}{7} (p^{7} r^{5})$ .

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Step 4.1

Combine $p^{7}$ and $\frac{6}{7}$ .

$\frac{p^{7} \cdot 6}{7} r^{5} z^{6} \cdot 14$

Step 4.2

Combine $\frac{p^{7} \cdot 6}{7}$ and $r^{5}$ .

$\frac{p^{7} \cdot 6 r^{5}}{7} z^{6} \cdot 14$

Step 5

Move $6$ to the left of $p^{7}$ .

$\frac{6 \cdot p^{7} r^{5}}{7} z^{6} \cdot 14$

Step 6

Combine $\frac{6 p^{7} r^{5}}{7}$ and $z^{6}$ .

$\frac{6 p^{7} r^{5} z^{6}}{7} \cdot 14$

Step 7

Cancel the common factor of $7$ .

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Step 7.1

Factor $7$ out of $14$ .

$\frac{6 p^{7} r^{5} z^{6}}{7} \cdot (7 (2))$

Step 7.2

Cancel the common factor.

$\frac{6 p^{7} r^{5} z^{6}}{7} \cdot (7 \cdot 2)$

Step 7.3

Rewrite the expression.

$6 p^{7} r^{5} z^{6} \cdot 2$

Step 8

Multiply $2$ by $6$ .

$12 p^{7} r^{5} z^{6}$