Question
S. Write each power as a product of repeated factors then tevaluate the power. \( \begin{array}{lll}\text { a. }\left(\frac{1}{3}\right)^{3} & \text { b. } 10^{4} & \text { c. }(0.8)^{2}\end{array} \)
Ask by Marshall Tucker. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
a. (1/3)³ = 1/27
b. 10⁴ = 10,000
c. (0.8)² = 0.64
Solution
a. Write (1/3)³ as (1/3) × (1/3) × (1/3). Multiplying the numerators and denominators gives 1/27.
b. Write 10⁴ as 10 × 10 × 10 × 10. Multiplying these together gives 10,000.
c. Write (0.8)² as 0.8 × 0.8. Multiplying these together gives 0.64.
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Simplify this solution Mind Expander
Let’s break these down and tackle them one by one! For \( \left(\frac{1}{3}\right)^{3} \), you can express this as \( \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \). When you multiply those together, you get \( \frac{1}{27} \). For \( 10^{4} \), this can be written as \( 10 \times 10 \times 10 \times 10 \). Evaluating this gives you \( 10,000 \). Finally, for \( (0.8)^{2} \), it becomes \( 0.8 \times 0.8 \). Multiplying those out gives you \( 0.64 \). So, putting it all together: a. \( \left(\frac{1}{3}\right)^{3} = \frac{1}{27} \) b. \( 10^{4} = 10,000 \) c. \( (0.8)^{2} = 0.64 \)
