Question
Solve for \( x \): \( x^{\frac{2}{3}} = 9 \)
Ask by Gough Boyd. in South Africa
Jan 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solutions are \( x = -27 \) and \( x = 27 \).
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Mind Expander
To solve the equation \( x^{\frac{2}{3}} = 9 \), you can start by raising both sides to the power of \( \frac{3}{2} \) to isolate \( x \). This gives you: \[ x = 9^{\frac{3}{2}} \] Calculating \( 9^{\frac{3}{2}} \), we know that \( 9 \) can be represented as \( 3^2 \). So we have: \[ 9^{\frac{3}{2}} = (3^2)^{\frac{3}{2}} = 3^{2 \cdot \frac{3}{2}} = 3^3 = 27 \] Thus, the solution is: \[ x = 27 \]
