To solve the equation \( x^{2/3} = 64 \), we first need to isolate \( x \).
- Raise both sides of the equation to the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \):
\[ (x^{2/3})^{3/2} = 64^{3/2} \]
- This simplifies to:
\[ x^{(2/3) \cdot (3/2)} = 64^{3/2} \]
\[ x^1 = 64^{3/2} \]
- Now we calculate \( 64^{3/2} \). First, find \( 64^{1/2} \):
\[ 64^{1/2} = 8 \]
- Then, compute \( 8^3 \):
\[ 8^3 = 512 \]
- Thus, we have:
\[ x = 512 \]
So the solution to the equation \( x^{2/3} = 64 \) is \( \boxed{512} \).
1 answer