ay not use a calculator for this ex (2) \( \left(\frac{1}{2}\right)^{3} \) (5) \( \left(-\frac{2}{3}\right)^{2} \) (8) \( \left(1 \frac{1}{3}\right)^{3} \)
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Sure! Let's tackle these expressions step by step! To calculate \( \left(\frac{1}{2}\right)^{3} \), you multiply \( \frac{1}{2} \) by itself three times, which gives you: \[ \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8} \] Next, for \( \left(-\frac{2}{3}\right)^{2} \), squaring a negative fraction results in a positive one, so: \[ \left(-\frac{2}{3}\right) \times \left(-\frac{2}{3}\right) = \frac{4}{9} \] Lastly, for \( \left(1 \frac{1}{3}\right)^{3} \), first convert the mixed number to an improper fraction: \[ 1 \frac{1}{3} = \frac{4}{3} \] Now, cube it: \[ \left(\frac{4}{3}\right)^{3} = \frac{4 \times 4 \times 4}{3 \times 3 \times 3} = \frac{64}{27} \] So we have: 1. \( \left(\frac{1}{2}\right)^{3} = \frac{1}{8} \) 2. \( \left(-\frac{2}{3}\right)^{2} = \frac{4}{9} \) 3. \( \left(1 \frac{1}{3}\right)^{3} = \frac{64}{27} \)
