Pregunta
20. \( 343^{\frac{1}{3}} \) 21. \( 64^{\frac{2}{3}} \)
Ask by Stephens Donnelly. in the United States
Mar 10,2025
Solución de inteligencia artificial de Upstudy
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\( 343^{\frac{1}{3}} = 7 \)
\( 64^{\frac{2}{3}} = 16 \)
Solución
**20. Evaluating \( 343^{\frac{1}{3}} \):**
1. Write \( 343 \) as a cube:
\( 343 = 7^3 \).
2. Apply the cube root:
\( 343^{\frac{1}{3}} = (7^3)^{\frac{1}{3}} \).
3. Use the exponent rule \((a^m)^{\frac{1}{n}} = a^{\frac{m}{n}}\):
\( (7^3)^{\frac{1}{3}} = 7^{3 \times \frac{1}{3}} = 7^1 = 7 \).
**21. Evaluating \( 64^{\frac{2}{3}} \):**
1. Write \( 64 \) as a cube:
\( 64 = 4^3 \).
2. Rewrite the expression using exponents:
\( 64^{\frac{2}{3}} = (4^3)^{\frac{2}{3}} \).
3. Apply the exponent rule:
\( (4^3)^{\frac{2}{3}} = 4^{3 \times \frac{2}{3}} = 4^2 \).
4. Calculate \( 4^2 \):
\( 4^2 = 16 \).
Thus, the answers are:
- \( 343^{\frac{1}{3}} = 7 \)
- \( 64^{\frac{2}{3}} = 16 \)
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Simplifique esta solución Beyond the Answer
To find \( 343^{\frac{1}{3}} \), you're looking for a number that, when multiplied by itself three times, equals 343. And guess what? That number is 7, since \( 7 \times 7 \times 7 = 343 \). It’s like discovering the secret code to the number! Now for \( 64^{\frac{2}{3}} \), you can break it down into two steps. First, find the cube root of 64, which is 4 because \( 4 \times 4 \times 4 = 64 \). Then, take that result and square it: \( 4^2 = 16 \). So, voilà! The magic number is 16.
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