Simplify: $3^4 \cdot 2^0 \cdot 6^1$
Answer (1)
Evaluate 3 4 which equals 81 .
Evaluate 2 0 which equals 1 .
Evaluate 6 1 which equals 6 .
Multiply the results: 81 c d o t 1 c d o t 6 = 486 . The simplified expression is 486 .
Explanation
Understanding the Expression We are asked to simplify the expression 3 4 c d o t 2 0 c d o t 6 1 . This involves evaluating exponents and then performing multiplication.
Evaluating 3 4 First, let's evaluate 3 4 . This means 3 multiplied by itself four times: 3 4 = 3 c d o t 3 c d o t 3 c d o t 3 = 81
Evaluating 2 0 Next, we evaluate 2 0 . Any non-zero number raised to the power of 0 is 1 . Therefore, 2 0 = 1
Evaluating 6 1 Now, we evaluate 6 1 . Any number raised to the power of 1 is the number itself. So, 6 1 = 6
Multiplying the Results Finally, we multiply the results together: 81 c d o t 1 c d o t 6 = 486
Final Answer So, the simplified expression is 486 .
Examples
Understanding exponents and simplification is crucial in many real-world scenarios. For instance, calculating compound interest involves exponential growth. If you invest money at a certain interest rate, the amount grows exponentially over time. Simplifying expressions like the one in this problem helps in determining the final value of such investments. Also, in computer science, understanding exponents is essential for analyzing the complexity of algorithms.
