Question
(2) \( 3^{-2} \cdot 3^{4}+\sqrt[4]{16}-\frac{3}{5} \cdot \frac{25}{9}= \)
Ask by Hills Ford. in Argentina
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
La expresión simplifica a \(9\frac{1}{3}\) o \(9.3\).
Solution
Calculate or simplify the expression \( 3^{-2} \cdot 3^{4}+\sqrt[4]{16}-\frac{3}{5} \cdot \frac{25}{9} \).
Calculate the value by following steps:
- step0: Calculate:
\(3^{-2}\times 3^{4}+\sqrt[4]{16}-\frac{3}{5}\times \frac{25}{9}\)
- step1: Simplify the root:
\(3^{-2}\times 3^{4}+2-\frac{3}{5}\times \frac{25}{9}\)
- step2: Multiply the numbers:
\(3^{2}+2-\frac{3}{5}\times \frac{25}{9}\)
- step3: Multiply the numbers:
\(3^{2}+2-\frac{5}{3}\)
- step4: Evaluate the power:
\(9+2-\frac{5}{3}\)
- step5: Add the numbers:
\(11-\frac{5}{3}\)
- step6: Reduce fractions to a common denominator:
\(\frac{11\times 3}{3}-\frac{5}{3}\)
- step7: Transform the expression:
\(\frac{11\times 3-5}{3}\)
- step8: Multiply the numbers:
\(\frac{33-5}{3}\)
- step9: Subtract the numbers:
\(\frac{28}{3}\)
La expresión \(3^{-2} \cdot 3^{4}+\sqrt[4]{16}-\frac{3}{5} \cdot \frac{25}{9}\) se simplifica a \(9\frac{1}{3}\) o \(9.3\).
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Simplify this solution Bonus Knowledge
Let's break it down step by step! First, calculate \( 3^{-2} \cdot 3^{4} \): Using the laws of exponents, \( 3^{-2} \cdot 3^{4} = 3^{-2 + 4} = 3^{2} = 9 \). Next, find \( \sqrt[4]{16} \): Since \( 16 = 2^4 \), we have \( \sqrt[4]{16} = 2 \). Now, calculate \( \frac{3}{5} \cdot \frac{25}{9} \): This gives \( \frac{3 \cdot 25}{5 \cdot 9} = \frac{75}{45} = \frac{5}{3} \). Putting it all together: \[ 9 + 2 - \frac{5}{3} = 11 - \frac{5}{3} \] To subtract, convert 11 to fractions: \[ 11 = \frac{33}{3} \rightarrow \frac{33}{3} - \frac{5}{3} = \frac{28}{3} \] So the final answer is \( \frac{28}{3} \) or approximately \( 9.33 \).
