Beck Murphy
09/09/2023 · Elementary School
Вычислите значение выраже \( \left(\sqrt[3]{(-5)^{3}}+\sqrt{(-8)^{2}}\right) \cdot \sqrt{3^{\frac{1}{4}} \cdot 3^{-\frac{9}{4}}} \)
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Tutor-Verified Answer
Step-by-step Solution
Calculate or simplify the expression \( \left(\sqrt[3]{(-5)^{3}}+\sqrt{(-8)^{2}}\right) \cdot \sqrt{3^{\frac{1}{4}} \cdot 3^{-\frac{9}{4}}} \).
Calculate the value by following steps:
- step0: Calculate:
\(\left(\sqrt[3]{\left(-5\right)^{3}}+\sqrt{\left(-8\right)^{2}}\right)\sqrt{3^{\frac{1}{4}}\times 3^{-\frac{9}{4}}}\)
- step1: Simplify the root:
\(\left(-5+\sqrt{\left(-8\right)^{2}}\right)\sqrt{3^{\frac{1}{4}}\times 3^{-\frac{9}{4}}}\)
- step2: Simplify the root:
\(\left(-5+\left|-8\right|\right)\sqrt{3^{\frac{1}{4}}\times 3^{-\frac{9}{4}}}\)
- step3: Calculate the absolute value:
\(\left(-5+8\right)\sqrt{3^{\frac{1}{4}}\times 3^{-\frac{9}{4}}}\)
- step4: Add the numbers:
\(3\sqrt{3^{\frac{1}{4}}\times 3^{-\frac{9}{4}}}\)
- step5: Multiply the numbers:
\(3\sqrt{3^{-2}}\)
- step6: Simplify the root:
\(3\times \frac{1}{3}\)
- step7: Reduce the numbers:
\(1\)
Значение выражения \( \left(\sqrt[3]{(-5)^{3}}+\sqrt{(-8)^{2}}\right) \cdot \sqrt{3^{\frac{1}{4}} \cdot 3^{-\frac{9}{4}}} \) равно 1.
Quick Answer
Значение выражения равно 1.
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