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Solve the exponential equation \( 2^{3x} = 64 \).
Express 64 as a power of 2: \( 64 = 2^6 \).
Therefore, \( 2^{3x} = 2^6 \).
Since the bases are the same, equate the exponents: \( 3x = 6 \).
Solving for \( x \), \( x = \frac{6}{3} = 2 \).
The diameter of the circle is equal to the side length of the square, which is 10 cm.
Thus, the radius \( r \) is \( \frac{10}{2} = 5 \) cm.
The area \( A \) of the circle is \( \pi r^2 = \pi \times 5^2 = 25\pi \) square cm.
Approximating, \( A \approx 25 \times 3.1416 = 78.54 \) square cm.
The probability of event A occurring is \( \frac{3}{5} \) and the probability of event B occurring is \( \frac{1}{2} \). If events A and B are independent, what is the probability of both A and B occurring?