Pregunta
7. Evaluate: \( \left(\frac{3}{11}\right)^{-1} \times\left(\frac{3}{11}\right)^{2} \times\left(\frac{3}{11}\right)^{3} \times\left(\frac{3}{11}\right)^{-4} \)
Ask by Cole Vaughan. in Papua New Guinea
Mar 18,2025
Solución de inteligencia artificial de Upstudy
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The result of the expression is 1.
Solución
Calculate or simplify the expression \( \left(\frac{3}{11}\right)^{-1} \times\left(\frac{3}{11}\right)^{2} \times\left(\frac{3}{11}\right)^{3} \times\left(\frac{3}{11}\right)^{-4} \).
Calculate the value by following steps:
- step0: Calculate:
\(\left(\frac{3}{11}\right)^{-1}\left(\frac{3}{11}\right)^{2}\left(\frac{3}{11}\right)^{3}\left(\frac{3}{11}\right)^{-4}\)
- step1: Multiply the terms:
\(\left(\frac{3}{11}\right)^{-1+2+3-4}\)
- step2: Calculate:
\(\left(\frac{3}{11}\right)^{0}\)
- step3: Evaluate the power:
\(1\)
The result of the expression \( \left(\frac{3}{11}\right)^{-1} \times\left(\frac{3}{11}\right)^{2} \times\left(\frac{3}{11}\right)^{3} \times\left(\frac{3}{11}\right)^{-4} \) is 1.
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Simplifique esta solución Beyond the Answer
To evaluate the expression \( \left(\frac{3}{11}\right)^{-1} \times\left(\frac{3}{11}\right)^{2} \times\left(\frac{3}{11}\right)^{3} \times\left(\frac{3}{11}\right)^{-4} \), we can use the property of exponents that states \( a^m \times a^n = a^{m+n} \). First, let's add the exponents together: \[ -1 + 2 + 3 - 4 \] Calculating these step by step: \[ -1 + 2 = 1, \] \[ 1 + 3 = 4, \] \[ 4 - 4 = 0. \] Now the expression simplifies to: \[ \left(\frac{3}{11}\right)^0. \] According to the rule that any non-zero number raised to the power of 0 is 1, we have: \[ \left(\frac{3}{11}\right)^0 = 1. \] Thus, the value of the given expression is: \[ \boxed{1}. \]
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