Pregunta
Evaluate. \( \sqrt[3]{729} \) \( 0^{4} \) \( 0^{3} \)
Ask by Simpson Reese. in the United States
Feb 28,2025
Solución de inteligencia artificial de Upstudy
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√[3](729) = 9, 0⁴ = 0, 0³ = 0
Solución
Let's evaluate each expression step by step:
1. For √[3](729):
We need the cube root of 729, which means finding the number that, when cubed, gives 729. Since 9 × 9 × 9 = 729, we have √[3](729) = 9.
2. For 0⁴:
Any non-negative power of 0 (except the ambiguous 0⁰) is 0. Thus, 0⁴ = 0.
3. For 0³:
Similarly, 0³ = 0.
So, the evaluated results are:
√[3](729) = 9
0⁴ = 0
0³ = 0
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Simplifique esta solución Beyond the Answer
The first expression, \( \sqrt[3]{729} \), evaluates to 9 because \( 9 \times 9 \times 9 = 729 \). This shows how finding cube roots can lead to interesting results with integer values. For the second expression, \( 0^{4} \), it equals 0 because any non-negative number raised to the power of zero is defined to be 1, but zero raised to any positive power is simply zero. Similarly, \( 0^{3} \) also equals 0, highlighting the unique properties of zero in exponentiation.
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