Salazar Marshall
04/11/2024 · Junior High School
13. Halle el valor de: \( \left(\frac{2}{3}\right)^{20} \times \frac{3^{22}}{2^{18}} \) \( \begin{array}{lllll}\text { A) } 16 & \text { B) } 27 & \text { C) } 24 & \text { D) } 36 & \text { E) } 42\end{array} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Calculate or simplify the expression \( (2/3)^{20} * 3^{22} / 2^{18} \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{\left(\frac{2}{3}\right)^{20}\times 3^{22}}{2^{18}}\)
- step1: Simplify:
\(\frac{\frac{2^{20}}{3^{20}}\times 3^{22}}{2^{18}}\)
- step2: Rewrite the expression:
\(\frac{\frac{2^{20}\times 3^{22}}{3^{20}}}{2^{18}}\)
- step3: Multiply by the reciprocal:
\(\frac{2^{20}\times 3^{22}}{3^{20}}\times \frac{1}{2^{18}}\)
- step4: Reduce the numbers:
\(\frac{2^{2}\times 3^{22}}{3^{20}}\)
- step5: Reduce the fraction:
\(2^{2}\times 3^{2}\)
- step6: Calculate:
\(6^{2}\)
- step7: Evaluate the power:
\(36\)
El valor de \( \left(\frac{2}{3}\right)^{20} \times \frac{3^{22}}{2^{18}} \) es 36. Por lo tanto, la respuesta correcta es la opción D) 36.
Quick Answer
El valor de la expresión es 36. La respuesta correcta es D) 36.
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit