Question
7. Solve for \( x \) : a) \( x^{\frac{2}{3}}=16 \)
Ask by Vega Erickson. in South Africa
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solutions are \(x=-64\) and \(x=64\).
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Bonus Knowledge
To solve \( x^{\frac{2}{3}} = 16 \), start by raising both sides to the power of \( \frac{3}{2} \). This cancels out the exponent on the left side: \[ x = 16^{\frac{3}{2}}. \] Now, calculate \( 16^{\frac{3}{2}} \): First, find \( 16^{\frac{1}{2}} = 4 \); then, raise it to the power of 3: \[ 4^3 = 64. \] Therefore, \( x = 64 \). So, the solution is \( x = 64 \).
