Simplify (p^5r^2)^4(-7p^3r^4)^2(6pr^3)

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

Rewrite using the commutative property of multiplication.

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

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

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

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

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

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

Multiply $5$ by $4$ .

$6 (p^{20} {(r^{2})}^{4}) {(- 7 p^{3} r^{4})}^{2} (p r^{3})$

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

Move $p$ .

$6 (p \cdot p^{20} {(r^{2})}^{4}) {(- 7 p^{3} r^{4})}^{2} r^{3}$

Multiply $p$ by $p^{20}$ .

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

$6 (p^{1} p^{20} {(r^{2})}^{4}) {(- 7 p^{3} r^{4})}^{2} r^{3}$

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

$6 (p^{1 + 20} {(r^{2})}^{4}) {(- 7 p^{3} r^{4})}^{2} r^{3}$

Add $1$ and $20$ .

$6 (p^{21} {(r^{2})}^{4}) {(- 7 p^{3} r^{4})}^{2} r^{3}$

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

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

$6 (p^{21} r^{2 \cdot 4}) {(- 7 p^{3} r^{4})}^{2} r^{3}$

Multiply $2$ by $4$ .

$6 (p^{21} r^{8}) {(- 7 p^{3} r^{4})}^{2} r^{3}$

Multiply $r^{8}$ by $r^{3}$ by adding the exponents.

Move $r^{3}$ .

$6 (p^{21} (r^{3} r^{8})) {(- 7 p^{3} r^{4})}^{2}$

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

$6 (p^{21} r^{3 + 8}) {(- 7 p^{3} r^{4})}^{2}$

Add $3$ and $8$ .

$6 (p^{21} r^{11}) {(- 7 p^{3} r^{4})}^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- 7 p^{3} r^{4}$ .

$6 p^{21} r^{11} ({(- 7 p^{3})}^{2} {(r^{4})}^{2})$

Apply the product rule to $- 7 p^{3}$ .

$6 p^{21} r^{11} ({(- 7)}^{2} {(p^{3})}^{2} {(r^{4})}^{2})$

Raise $- 7$ to the power of $2$ .

$6 p^{21} r^{11} (49 {(p^{3})}^{2} {(r^{4})}^{2})$

Multiply the exponents in ${(p^{3})}^{2}$ .

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

$6 p^{21} r^{11} (49 p^{3 \cdot 2} {(r^{4})}^{2})$

Multiply $3$ by $2$ .

$6 p^{21} r^{11} (49 p^{6} {(r^{4})}^{2})$

Multiply $p^{21}$ by $p^{6}$ by adding the exponents.

Move $p^{6}$ .

$6 (p^{6} p^{21}) r^{11} (49 {(r^{4})}^{2})$

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

$6 p^{6 + 21} r^{11} (49 {(r^{4})}^{2})$

Add $6$ and $21$ .

$6 p^{27} r^{11} (49 {(r^{4})}^{2})$

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

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

$6 p^{27} r^{11} (49 r^{4 \cdot 2})$

Multiply $4$ by $2$ .

$6 p^{27} r^{11} (49 r^{8})$

Multiply $r^{11}$ by $r^{8}$ by adding the exponents.

Move $r^{8}$ .

$6 p^{27} (r^{8} r^{11}) \cdot 49$

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

$6 p^{27} r^{8 + 11} \cdot 49$

Add $8$ and $11$ .

$6 p^{27} r^{19} \cdot 49$

Multiply $49$ by $6$ .

$294 p^{27} r^{19}$

Simplify (p^5r^2)^4(-7p^3r^4)^2(6pr^3)

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