Simplify (-(35p^6q^8)/(5r^-5))^2

${(- \frac{35 p^{6} q^{8}}{5 r^{- 5}})}^{2}$

Step 1

Move $r^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(- \frac{35 p^{6} q^{8} r^{5}}{5})}^{2}$

Step 2

Cancel the common factor of $35$ and $5$ .

Factor $5$ out of $35 p^{6} q^{8} r^{5}$ .

${(- \frac{5 (7 p^{6} q^{8} r^{5})}{5})}^{2}$

Cancel the common factors.

Factor $5$ out of $5$ .

${(- \frac{5 (7 p^{6} q^{8} r^{5})}{5 (1)})}^{2}$

Cancel the common factor.

${(- \frac{5 (7 p^{6} q^{8} r^{5})}{5 \cdot 1})}^{2}$

Rewrite the expression.

${(- \frac{7 p^{6} q^{8} r^{5}}{1})}^{2}$

Divide $7 p^{6} q^{8} r^{5}$ by $1$ .

${(- (7 p^{6} q^{8} r^{5}))}^{2}$

Step 3

Multiply $7$ by $- 1$ .

${(- 7 (p^{6} q^{8} r^{5}))}^{2}$

Step 4

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

Apply the product rule to $- 7 p^{6} q^{8} r^{5}$ .

${(- 7 p^{6} q^{8})}^{2} {(r^{5})}^{2}$

Apply the product rule to $- 7 p^{6} q^{8}$ .

${(- 7 p^{6})}^{2} {(q^{8})}^{2} {(r^{5})}^{2}$

Apply the product rule to $- 7 p^{6}$ .

${(- 7)}^{2} {(p^{6})}^{2} {(q^{8})}^{2} {(r^{5})}^{2}$

Step 5

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

$49 {(p^{6})}^{2} {(q^{8})}^{2} {(r^{5})}^{2}$

Step 6

Multiply the exponents in ${(p^{6})}^{2}$ .

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

$49 p^{6 \cdot 2} {(q^{8})}^{2} {(r^{5})}^{2}$

Multiply $6$ by $2$ .

$49 p^{12} {(q^{8})}^{2} {(r^{5})}^{2}$

Step 7

Multiply the exponents in ${(q^{8})}^{2}$ .

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

$49 p^{12} q^{8 \cdot 2} {(r^{5})}^{2}$

Multiply $8$ by $2$ .

$49 p^{12} q^{16} {(r^{5})}^{2}$

Step 8

Multiply the exponents in ${(r^{5})}^{2}$ .

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

$49 p^{12} q^{16} r^{5 \cdot 2}$

Multiply $5$ by $2$ .

$49 p^{12} q^{16} r^{10}$

Simplify (-(35p^6q^8)/(5r^-5))^2

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