Solve each equation. $$ \frac{1}{512}=p^{-\frac{3}{2}} $$

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Solve the equation $$ \frac{1}{512}=p^{-\frac{3}{2}} $$.
Solve the equation by following steps:
- step0: Solve for $$p$$:
  $$\frac{1}{512}=p^{-\frac{3}{2}}$$
- step1: Find the domain:
  $$\frac{1}{512}=p^{-\frac{3}{2}},p>0$$
- step2: Swap the sides:
  $$p^{-\frac{3}{2}}=\frac{1}{512}$$
- step3: Rewrite the expression:
  $$\frac{1}{p^{\frac{3}{2}}}=\frac{1}{512}$$
- step4: Rewrite the expression:
  $$p^{\frac{3}{2}}=512$$
- step5: Raise both sides to the $$\frac{2}{3}$$-th power$$:$$
  $$\left(p^{\frac{3}{2}}\right)^{\frac{2}{3}}=512^{\frac{2}{3}}$$
- step6: Evaluate the power:
  $$p=64$$
- step7: Check if the solution is in the defined range:
  $$p=64,p>0$$
- step8: Find the intersection:
  $$p=64$$
- step9: Check the solution:
  $$p=64$$
The solution to the equation $$ \frac{1}{512}=p^{-\frac{3}{2}} $$ is $$ p=64 $$.
$$ p=64 $$

Solve each equation.

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