Wood Rogers
09/22/2023 · Primary School
1. ¿Cuál es el valor de \( \frac{(-3)^{-1} \cdot 2^{3}}{6^{2}} \) ? A) \( -\frac{2}{27} \) B) -1 C) \( \frac{2}{3} \) D) \( \frac{3}{2} \)
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Tutor-Verified Answer
Step-by-step Solution
Calculate or simplify the expression \( (-3)^{-1} \cdot 2^{3} / 6^{2} \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{\left(-3\right)^{-1}\times 2^{3}}{6^{2}}\)
- step1: Factor the expression:
\(\frac{\left(-3\right)^{-1}\times 2^{3}}{2^{2}\times 3^{2}}\)
- step2: Reduce the fraction:
\(\frac{\left(-3\right)^{-1}\times 2}{3^{2}}\)
- step3: Determine the sign:
\(\frac{-3^{-1}\times 2}{3^{2}}\)
- step4: Calculate:
\(-\frac{\frac{2}{3}}{3^{2}}\)
- step5: Reduce the fraction:
\(\frac{-\frac{2}{3}}{3^{2}}\)
- step6: Evaluate the power:
\(\frac{-\frac{2}{3}}{9}\)
- step7: Multiply by the reciprocal:
\(-\frac{2}{3}\times \frac{1}{9}\)
- step8: Multiply the fractions:
\(-\frac{2}{3\times 9}\)
- step9: Multiply:
\(-\frac{2}{27}\)
El valor de \( \frac{(-3)^{-1} \cdot 2^{3}}{6^{2}} \) es aproximadamente -0.0744. Por lo tanto, la respuesta correcta es A) \( -\frac{2}{27} \).
Quick Answer
El valor de \( \frac{(-3)^{-1} \cdot 2^{3}}{6^{2}} \) es A) \( -\frac{2}{27} \).
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