Simplify ((-8p^10)/(7r^3))^2

${(\frac{- 8 p^{10}}{7 r^{3}})}^{2}$

Step 1

Move the negative in front of the fraction.

${(- \frac{(8) p^{10}}{7 r^{3}})}^{2}$

Step 2

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

Apply the product rule to $- \frac{8 p^{10}}{7 r^{3}}$ .

${(- 1)}^{2} {(\frac{8 p^{10}}{7 r^{3}})}^{2}$

Apply the product rule to $\frac{8 p^{10}}{7 r^{3}}$ .

${(- 1)}^{2} \frac{{(8 p^{10})}^{2}}{{(7 r^{3})}^{2}}$

Apply the product rule to $8 p^{10}$ .

${(- 1)}^{2} \frac{8^{2} {(p^{10})}^{2}}{{(7 r^{3})}^{2}}$

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

${(- 1)}^{2} \frac{8^{2} {(p^{10})}^{2}}{7^{2} {(r^{3})}^{2}}$

Step 3

Simplify the expression.

Raise $- 1$ to the power of $2$ .

$1 \frac{8^{2} {(p^{10})}^{2}}{7^{2} {(r^{3})}^{2}}$

Multiply $\frac{8^{2} {(p^{10})}^{2}}{7^{2} {(r^{3})}^{2}}$ by $1$ .

$\frac{8^{2} {(p^{10})}^{2}}{7^{2} {(r^{3})}^{2}}$

Step 4

Simplify the numerator.

Raise $8$ to the power of $2$ .

$\frac{64 {(p^{10})}^{2}}{7^{2} {(r^{3})}^{2}}$

Multiply the exponents in ${(p^{10})}^{2}$ .

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

$\frac{64 p^{10 \cdot 2}}{7^{2} {(r^{3})}^{2}}$

Multiply $10$ by $2$ .

$\frac{64 p^{20}}{7^{2} {(r^{3})}^{2}}$

Step 5

Simplify the denominator.

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

$\frac{64 p^{20}}{49 {(r^{3})}^{2}}$

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

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

$\frac{64 p^{20}}{49 r^{3 \cdot 2}}$

Multiply $3$ by $2$ .

$\frac{64 p^{20}}{49 r^{6}}$