Question
\( \frac{-2}{5}, \frac{2}{3}, \frac{7}{15} \), 20. Solve \( :\left\{\left(3^{3}\right)^{2} \times 3^{3} \div 3^{7}\right\}+3^{0} \)
Ask by Clark Cook. in India
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The answer is 10.
Solution
Calculate or simplify the expression \( (3^3)^2 * 3^3 / 3^7 + 3^0 \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{\left(3^{3}\right)^{2}\times 3^{3}}{3^{7}}+3^{0}\)
- step1: Evaluate the power:
\(\frac{\left(3^{3}\right)^{2}\times 3^{3}}{3^{7}}+1\)
- step2: Multiply by \(a^{-n}:\)
\(\left(3^{3}\right)^{2}\times 3^{3}\times 3^{-7}+1\)
- step3: Multiply the exponents:
\(3^{3\times 2}\times 3^{3}\times 3^{-7}+1\)
- step4: Multiply the numbers:
\(3^{6}\times 3^{3}\times 3^{-7}+1\)
- step5: Multiply:
\(3^{2}+1\)
- step6: Evaluate the power:
\(9+1\)
- step7: Add the numbers:
\(10\)
The solution to the expression \( \left\{\left(3^{3}\right)^{2} \times 3^{3} \div 3^{7}\right\}+3^{0} \) is 10.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
First, let’s simplify the expression step by step. Start with the nested expression: \((3^3)^2\) simplifies to \(3^{3 \times 2} = 3^6\). Now substitute back into the original equation: \[ \left\{3^6 \times 3^3 \div 3^7\right\} \] Using the laws of exponents, we can combine the multiplication first: \(3^6 \times 3^3 = 3^{6 + 3} = 3^9\). Next, divide by \(3^7\): \[ 3^9 \div 3^7 = 3^{9 - 7} = 3^2 \] Now, simplify \(3^2 = 9\). Don't forget about the \(+3^0\), which equals \(1\): So, we add: \[9 + 1 = 10.\] The final answer is: \[ \boxed{10}. \]
