Algebra Examples

${(p^{5} r^{2})}^{4} (- 7 p^{3} r^{4}) (6 p r^{3})$

Step 1

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

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Step 1.1

Move $p$ .

${(p^{5} r^{2})}^{4} (- 7 (p \cdot p^{3}) r^{4}) (6 r^{3})$

Step 1.2

Multiply $p$ by $p^{3}$ .

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Step 1.2.1

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

${(p^{5} r^{2})}^{4} (- 7 (p^{1} p^{3}) r^{4}) (6 r^{3})$

Step 1.2.2

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

${(p^{5} r^{2})}^{4} (- 7 p^{1 + 3} r^{4}) (6 r^{3})$

Step 1.3

Add $1$ and $3$ .

${(p^{5} r^{2})}^{4} (- 7 p^{4} r^{4}) (6 r^{3})$

Step 2

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

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Step 2.1

Move $r^{3}$ .

${(p^{5} r^{2})}^{4} (- 7 p^{4} (r^{3} r^{4})) \cdot 6$

Step 2.2

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

${(p^{5} r^{2})}^{4} (- 7 p^{4} r^{3 + 4}) \cdot 6$

Step 2.3

Add $3$ and $4$ .

${(p^{5} r^{2})}^{4} (- 7 p^{4} r^{7}) \cdot 6$

Step 3

Rewrite using the commutative property of multiplication.

$- 7 {(p^{5} r^{2})}^{4} p^{4} r^{7} \cdot 6$

Step 4

Apply the product rule to $p^{5} r^{2}$ .

$- 7 ({(p^{5})}^{4} {(r^{2})}^{4}) p^{4} r^{7} \cdot 6$

Step 5

Multiply the exponents in ${(p^{5})}^{4}$ .

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Step 5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 7 (p^{5 \cdot 4} {(r^{2})}^{4}) p^{4} r^{7} \cdot 6$

Step 5.2

Multiply $5$ by $4$ .

$- 7 (p^{20} {(r^{2})}^{4}) p^{4} r^{7} \cdot 6$

Step 6

Multiply $p^{20}$ by $p^{4}$ by adding the exponents.

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Step 6.1

Move $p^{4}$ .

$- 7 (p^{4} p^{20} {(r^{2})}^{4}) r^{7} \cdot 6$

Step 6.2

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

$- 7 (p^{4 + 20} {(r^{2})}^{4}) r^{7} \cdot 6$

Step 6.3

Add $4$ and $20$ .

$- 7 (p^{24} {(r^{2})}^{4}) r^{7} \cdot 6$

Step 7

Multiply the exponents in ${(r^{2})}^{4}$ .

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Step 7.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 7 (p^{24} r^{2 \cdot 4}) r^{7} \cdot 6$

Step 7.2

Multiply $2$ by $4$ .

$- 7 (p^{24} r^{8}) r^{7} \cdot 6$

Step 8

Multiply $r^{8}$ by $r^{7}$ by adding the exponents.

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Step 8.1

Move $r^{7}$ .

$- 7 (p^{24} (r^{7} r^{8})) \cdot 6$

Step 8.2

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

$- 7 (p^{24} r^{7 + 8}) \cdot 6$

Step 8.3

Add $7$ and $8$ .

$- 7 (p^{24} r^{15}) \cdot 6$

Step 9

Multiply $6$ by $- 7$ .

$- 42 p^{24} r^{15}$